Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am a little confused about composition of logarithms, I am given $f(x)=5^{2+5x}$ and $g(x)=\log_5 x$ and I am supposed to find $f(g(x))$. Here is what I have done so far, $$5^{2+5(\log_5 x)}$$ $$5^{2+5\log_x 5}$$

I am stuck on this step because I don't know how to cancel the log in the exponent. Since it's $5\log_5 x$ and not $5^{\log_5 x}$. Could anyone explain how I would simplify this problem?

share|improve this question
add comment

1 Answer

up vote 2 down vote accepted

If you recall, there are several important properties of logarithm. One of them, which your class should have mentioned, is that $p \log_b{x} = \log_b(x^p)$ for any choices of $x > 0$, real number $p$, and base $b$. This should allow you to simplify your problem in the following way:

$$5^{2 + 5 \log_5{x}} = 5^{2 + \log_5{x^5}}$$ Now, remember that whenever we have $x^{a + b}$, we can break it up into $x^{a+b} = (x^a)(x^b)$.

share|improve this answer
    
I tried moving the 5 to the exponent for $log_{5}x$ but I am still stuck. What am I supposed to do now? –  Kot Oct 5 '12 at 0:35
    
@StevenN, I've elaborated a little bit more above. –  Christopher A. Wong Oct 5 '12 at 0:39
    
Wow, I forgot about that property. Thank you for reminding me of it :). I understand how to solve this now. –  Kot Oct 5 '12 at 0:47
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.