2( log 2 x − log y ) − ( log 3 + 2 log 5)

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2( log 2 x − log y ) − ( log 3 + 2 log 5)

Mathematics
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what are you supposed to do about it?
solve it
it is not an equation. you cant solve it.

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Other answers:

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

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