anonymous
  • anonymous
2( log 2 x − log y ) − ( log 3 + 2 log 5)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
what are you supposed to do about it?
anonymous
  • anonymous
solve it
anonymous
  • anonymous
it is not an equation. you cant solve it.

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anonymous
  • anonymous
cant it be simplified?
anonymous
  • anonymous
You want to simplify it?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Is it log (2x), or log x to base 2?
anonymous
  • anonymous
it is log((2x/y)^2)-log 75
anonymous
  • anonymous
log 2x
anonymous
  • anonymous
not that log a - log b = log(a/b) and log a +log b = log(ab)
anonymous
  • anonymous
how did u get the answer dhatraditya?
anonymous
  • anonymous
note*
anonymous
  • anonymous
note also that xlog a = log a^x
anonymous
  • anonymous
\[2 (\log(2x)-\log y)-(\log 3+2\log 5)=2(\log {2x \over y})-\log(3*5^2)\] =\[\log({2x \over y})^2-\log(75)=\log({4x^2 \over 75y^2})\]
anonymous
  • anonymous
I think this is the simplest it can be.
anonymous
  • anonymous
so its simplified form is log ((2x/y)^2/75))
anonymous
  • anonymous
What AnwarA has.
anonymous
  • anonymous
thank you so much
anonymous
  • anonymous
You're welcome!
anonymous
  • anonymous
how did u get the 75?
anonymous
  • anonymous
3*5^2=3(25)=75
anonymous
  • anonymous
as I explained, x log a = log a^x so 2 log 5 = log 5^2 = log 25 log a + log b = log (ab) now, log 3+ log 25 = log (3 times25) = log 75
anonymous
  • anonymous
i understand now.thx
anonymous
  • anonymous
you are welcome.
anonymous
  • anonymous
solve log base x (5x+24)=2
anonymous
  • anonymous
x = 8 or -3
anonymous
  • anonymous
since logs are not defined for negative numbers, x = 8
anonymous
  • anonymous
do you know how I arrived at the answer, leona?
anonymous
  • anonymous
?how did u work it out
anonymous
  • anonymous
do you know how logarithms work?
anonymous
  • anonymous
i know some of the rules
anonymous
  • anonymous
tell me what you know about logs? what do you understand by logs?
anonymous
  • anonymous
i know that the logarithm of 1 regardless of the base is one
anonymous
  • anonymous
if i told you log 32 to the base 4 is 2.5, what do I mean by that?
anonymous
  • anonymous
that 4 ^2.5 is 32
anonymous
  • anonymous
exactly! good! have you tried that in your calculator?
anonymous
  • anonymous
yes
anonymous
  • anonymous
so you understand that any number can be represented as a power of another number?
anonymous
  • anonymous
yes
anonymous
  • anonymous
okay good. so what do i mean when i say log(5x+24) to the base x is 2?
anonymous
  • anonymous
it means that x raise to the power 2 equal (5x+24)
anonymous
  • anonymous
I should have said any POSITIVE number can be represented as apower of any other number (the base)
anonymous
  • anonymous
right, so x^2 = 5x+24
anonymous
  • anonymous
this is a simple quadratic equation
anonymous
  • anonymous
should i square the x^2?
anonymous
  • anonymous
why would you want to do that?
anonymous
  • anonymous
i dont know how to remove the x
anonymous
  • anonymous
okay have you solved quadratic equations before?
anonymous
  • anonymous
yes
anonymous
  • anonymous
can you see that x^2 = 5x+24 can be rearranged so that it is in the form ax^2+bx+c = 0?
anonymous
  • anonymous
ohh yea
anonymous
  • anonymous
after that it is straightforward factoring. Remember that you will get a negative root. You cannot use the negative root, because as I explained before, logarithms for negative bases are generally discarded.
anonymous
  • anonymous
what r the two factors? cant find them
anonymous
  • anonymous
post your equation.
anonymous
  • anonymous
x^2-5x-24=0
anonymous
  • anonymous
i got 8
anonymous
  • anonymous
yeah!!!!!!
anonymous
  • anonymous
did you use the quadratic formula or the factoring method?
anonymous
  • anonymous
quadratic
anonymous
  • anonymous
okay. anything that works, although in this case factoring is more elegant and efficient. remember, you have to discard the x= -3 root
anonymous
  • anonymous
i did
anonymous
  • anonymous
okay, do you know the reason why you discarded -3?
anonymous
  • anonymous
because log not defined for negative numbers
anonymous
  • anonymous
no, its because logs with negative bases only work for even powers. anyway, good job! have a medal.
anonymous
  • anonymous
ok thank you
anonymous
  • anonymous
do a little homework assignment for me. Google "why logarithms are not defined for negative bases" and "why logarithms are not defined for negative numbers". it will help you understand logs much better. all the best!
anonymous
  • anonymous
you are welcome.
anonymous
  • anonymous
ill do that
anonymous
  • anonymous
:)
anonymous
  • anonymous
are u going to be online in the night?
anonymous
  • anonymous
i dont know. I generally come here in my free time to help out.
anonymous
  • anonymous
ohh cause i ave exam 2marow and i need more help with other topics
anonymous
  • anonymous
oh.. you can post your questions here so that I get notifications and I'll try to answer them before tomorrow.
anonymous
  • anonymous
ok am going to try this question log base x (5x+14)=2
anonymous
  • anonymous
okay, lemme know how it works out. you should get 7
anonymous
  • anonymous
logarithm are not defined for negative values because the log and In graphs have a vertical asymptotic line at x=0 which is the lower boundary of the graph ..in fact the limit as x approaches zero from the right hand side ,the function approaches infinity and that makes the zero point the maximum tolerable value for the x values less than zero
anonymous
  • anonymous
i got 7....using the factoring method
anonymous
  • anonymous
okay good.
anonymous
  • anonymous
thank you
anonymous
  • anonymous
your latest logarithm question will go like : \[5x +14=x^{2}\]
anonymous
  • anonymous
so \[x ^{2}-5x-14=0 and then you solve with the quadratic formula \]
anonymous
  • anonymous
need help with this 1....log base 4 (1) +log (25)
anonymous
  • anonymous
so x= 7 or x=-2 but when you substitute the x=-2 the equation doesnt make sence so x=7 is the answer hope that was helpful
anonymous
  • anonymous
okay, what does log base 4 (1) mean?
anonymous
  • anonymous
log to base 4 to a number = 1
anonymous
  • anonymous
log base 4 of 1 means what power will you raise the number 4 to have a value of 1 so its like : 1=4\[^{x}\]
anonymous
  • anonymous
it means that 4 raised to a number should be equal to 1. what is that number? we know that any number raised to the power 0 is 1. so log base 4 (1) is 0. so your equation simplifies to just log 25
anonymous
  • anonymous
like 4\[4^{x}=1 \]
anonymous
  • anonymous
that means x=0
anonymous
  • anonymous
because
anonymous
  • anonymous
\[4^{0}\]
anonymous
  • anonymous
ohh yeah thats a rule of logs
anonymous
  • anonymous
yes. you should remember the basic rules of logs. Also, understand what logarithms mean. That way, even if you get stuck in your test, you can work it out.
anonymous
  • anonymous
so 5^2=25
anonymous
  • anonymous
right, log 25 = log 5^2 = ?
anonymous
  • anonymous
yeah so the final answer is log 5^2=25
anonymous
  • anonymous
log 25 without a base specified means the base is a standard base of ten (10)
anonymous
  • anonymous
so are you saying that 10^25 = 5^2, leona?
anonymous
  • anonymous
so it shd read like \[\log_{10} 25=x\]
anonymous
  • anonymous
which means 25=\[10^{x}\]
anonymous
  • anonymous
no am nt
anonymous
  • anonymous
then what do yoou mean by log 5^2 = 25?
anonymous
  • anonymous
sinse it doent ave a base its base 10 rite?
anonymous
  • anonymous
so x=\[x= \log 25/\log 10\]
anonymous
  • anonymous
yes, we assume that the base is 10 if it is not specified
anonymous
  • anonymous
yas since it doesnt have any base it means base ten ...youre rite
anonymous
  • anonymous
so i should use the rule of change of base
anonymous
  • anonymous
log 25 is simply log 5^2 = 2log5
anonymous
  • anonymous
are you required to find the numerical value of log 25?
anonymous
  • anonymous
if you are, just punch it in your calculator and you have your answer.
anonymous
  • anonymous
no that was nt required
anonymous
  • anonymous
then it is simply log 25, which can be written as 2 log 5
anonymous
  • anonymous
ok..
anonymous
  • anonymous
since we know that x log a = log a^x
anonymous
  • anonymous
ok i now understand that rule
anonymous
  • anonymous
2logx-log(2+3x)=1
anonymous
  • anonymous
okay, use the identities. x log a = log a^x and log a - log b = log(a/b)
anonymous
  • anonymous
ok
anonymous
  • anonymous
take it one step at a time. what is 2 log x = ?
anonymous
  • anonymous
log x^2
anonymous
  • anonymous
okay and what is log x^2-log(2+3x)?
anonymous
  • anonymous
would it be base 10 since no base is given?
anonymous
  • anonymous
yes
anonymous
  • anonymous
10^1
anonymous
  • anonymous
is zero
anonymous
  • anonymous
no, i meant log a - log b is log(a/b) so log (x^2) = log (2+3x) = ?
anonymous
  • anonymous
sorry log (x^2) - log (2+3x) = ?
anonymous
  • anonymous
am stuck
anonymous
  • anonymous
okay it is log(x^2/(2+3x)
anonymous
  • anonymous
so log (x^2/(2+3x)) = 1
anonymous
  • anonymous
yes
anonymous
  • anonymous
so if log A to the base 10 is 1, what do i mean by that?
anonymous
  • anonymous
10^1=a
anonymous
  • anonymous
yes, so if i say log(x^2/(2+3x)) = 1, what do i mean by that?
anonymous
  • anonymous
it means log 1 = x^2/2+3x
anonymous
  • anonymous
no, pay attention to the last two statements i made and post your answer. think about it carefully.
anonymous
  • anonymous
i still dont get it
anonymous
  • anonymous
if log a = 1 means a = 10^1 then log(x^2/(2+3x)) =1 means x^2/2+3x = 10^1
anonymous
  • anonymous
ohhhhhhhh...:)
anonymous
  • anonymous
now its just a quadratic equation. solve it and find the values of x
anonymous
  • anonymous
rearrange it for me plz
anonymous
  • anonymous
no, you can do this on your own. multiply both sides by 2+3x and post what you got.
anonymous
  • anonymous
4+12x+9x^2=20 +30x
anonymous
  • anonymous
\[x ^{2}/(2+3x) = 10\]
anonymous
  • anonymous
multiply both sides by (2+3x) to get \[x ^{2} = 30x+20\]
anonymous
  • anonymous
yea i ave that down
anonymous
  • anonymous
I dont understand how you got 4+12x+9x^2=20 +30x
anonymous
  • anonymous
do you know how to manipulate equations?
anonymous
  • anonymous
no
anonymous
  • anonymous
i get it now
anonymous
  • anonymous
http://www.chem.tamu.edu/class/fyp/mathrev/mr-algeb.html
anonymous
  • anonymous
ok

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