Could somebody help me with this log problem?

- UnknownRandom

Could somebody help me with this log problem?

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- cutiecomittee123

what is it

- UnknownRandom

4log4(3)-log4(4)

- UnknownRandom

The answer can't contain a log

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## More answers

- cutiecomittee123

I am really rusty and logs because I havent done them in a year or so. But I think you have to convert it to a diferent form inorder to solve it

- Nnesha

familiar with the log properties ?

- UnknownRandom

Yep.

- Nnesha

alright apply log property start with the power rule

- UnknownRandom

log4(81/4)?

- Nnesha

looks good

- Nnesha

now set it equal to x
or use change of base formula

- Nnesha

if we set it equal to x we should change log to exponential form

- UnknownRandom

I can't remember how to do that.

- Nnesha

for change of base formula \[\huge\rm log_b a = \frac{ \log a }{ \log b }\]

- Nnesha

and if you want to do it by hands so set it equal to x |dw:1443129484346:dw|

- UnknownRandom

|dw:1443129612389:dw|

- UnknownRandom

Is that right?

- UnknownRandom

Solving for that power?

- Nnesha

yes let missing exponent equal to x
and then write 81 in terms of base 4

- Nnesha

4 to the what power =81?

- UnknownRandom

Wait, why can you cancel that 4?

- UnknownRandom

in 81/4

- Nnesha

how would you cancel it ?

- UnknownRandom

How did you get rid of that 4 in 81/4?

- Nnesha

we should rewrite 81 in terms of base 4 so we can apply the exponent rule
\[\huge\rm \frac{ x^m }{ x^n }=x^{m-n}\]

- Nnesha

we need 4 base at the numerator so rewrite 81 in terms of base 4
4 to the what power = 81 ?

- Nnesha

alright wait a sec

- Nnesha

ahh i see we can't write 81 in terms of base 4
3^4 = 81 i was thinking 4^3 sorry about that

- Nnesha

well u have to take log to solve for x so jsut use change of base formula that would be easy

- UnknownRandom

I was lost. The application we use to answer questions won't take answers with log in it. So what do you recommend?

- Nnesha

change of base formula

- UnknownRandom

How do write that?

- UnknownRandom

*you

- Nnesha

\[\huge\rm \log_\color{blue}{b} \color{ReD}{a} =\frac{ \log\color{red}{ a} }{ \log \color{blue}{b} }\]

- UnknownRandom

log (81/4)/log(4)?

- Nnesha

good right!!

- UnknownRandom

Do you subtract the two now?

- Nnesha

subtract no just divide them
we don't need the original question

- UnknownRandom

True, but on our test we can't use calculators so I don't know how I would do that division without one.

- Nnesha

can't use calculator hm
i mean not just for log(4) ???

- UnknownRandom

Nope, but we will probably be able to use log in our answers on the test.

- Nnesha

we have to use calculator for this one bec 81/ 4 is a decimal answer
u were asking can we multiply 4 both sides ? yes you can |dw:1443130983953:dw|

- Nnesha

when we multiply same bases we should `add` exponents \[\huge\rm x^m \times x^n=x^{m+n}\]
\[\large\rm 4^1 \times 4^x =81 ~~~~~~~~~~4^{1+x}=81\]

- UnknownRandom

So how do you find x?

- Nnesha

now take log both sides to move the exponent at front \[ \huge\rm (1+x )\log(4) = \log (81)\] now u can solve for x

- Nnesha

divide both sides by log(4) and then subtract 1

- UnknownRandom

Ok, I got 2.169925001 but it said the answer was wrong.

- Nnesha

http://www.wolframalpha.com/input/?i=4log4%283%29-log4%284%29 that's the correct answer

- Nnesha

is there any statement round some hundred/thousandth ?

- UnknownRandom

Nope

- Nnesha

well i round it hundred place
2.169925001
(two numbers after decimal if the the 3rd is 5 or greater than 5 then we can wround to 7)
2.169925001
hundredths place 2.17

- Nnesha

did they gave u the right answer ?

- UnknownRandom

Nope :(

- Nnesha

ugh that's what i got
and that's exactly what on this calc http://www.wolframalpha.com/input/?i=4log4%283%29-log4%284%29

- UnknownRandom

I don't know then. Thanks for the help though.

- Nnesha

alright ask ur teacher
let me know what 's the correct answer if that's not right
good luck!

- UnknownRandom

I just typed 3/4 and it worked. Wow.... I guess the 4 wasn't supposed to be there on that problem. @Nnesha

- Nnesha

3/4 ? what 4 wasn't supposed to be there ?

- UnknownRandom

I guess not. Somebody done messed up.

- UnknownRandom

and wasted 2 hours of my life.

- Nnesha

i don't get it
so what was the question ?

- UnknownRandom

The question was evaluate 4*log4(3)-log4(4)

- Nnesha

so 4 isn't a base ?

- Nnesha

\[4 \log4(3) - \log4(4)\] like this or \[4\log_4 (3) - \log_4(4)\]

- UnknownRandom

The second one

- Nnesha

okay there is 4 at front of log
so we have to apply the power rule right

- UnknownRandom

Yep

- Nnesha

so \[\log_4 (3)^4 - \log_4 4 = \log_4 \frac{ (3)^4 }{ 4 }\] that's what we did so what was the mistake ? o.O hmm

- UnknownRandom

I think it was typed wrong and the 4 in the front shouldn't have been there.

- Nnesha

oh okay so \[\large\rm \log_4 \frac{ 3 }{ 4 }\]

- UnknownRandom

That's what I think.

- Nnesha

that will give u the negative answer

- Nnesha

we can just guess if we don't know what the question is exly

- UnknownRandom

\[4\log_4{3}-1 \]

- UnknownRandom

So \[\frac{ \log3 }{ \log4 }-1\]

- UnknownRandom

= -.208

- UnknownRandom

4^-.208 = 3/4

- UnknownRandom

@Nnesha

- UnknownRandom

4^log4(3)-log4(4) That is what the problem was supposed to say.

- Nnesha

take a screenshot plz
you're not sure abt the question ..

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