# Thread: help with logs

1. ## help with logs

I have two functions

f(x)=$\displaystyle 9^x$ and

g(x)=$\displaystyle log_{3}(x)$

I am asked to write h(x) = (f o g)(x). I thought this should be

$\displaystyle 9^ (log_{3}(x))$

Is this correct? How can we solve this? And the book is asking for a quadratic function, how can this be done? Thanks!

2. Originally Posted by andres
I have two functions

f(x)=$\displaystyle 9^x$ and

g(x)=$\displaystyle log_{3}(x)$

I am asked to write h(x) = (f o g)(x). I thought this should be

$\displaystyle 9^ (log_{3}(x))$

Is this correct? How can we solve this? And the book is asking for a quadratic function, how can this be done? Thanks!
$\displaystyle (f\, o\, g)(x) = f[g(x)] = 9^{log_3(x)}$ as you said

Here it's important to notice that $\displaystyle 9 = 3^2$

Using the laws of exponents and logs this simplifies to:

$\displaystyle (f\, o\, g)(x) = (3^2)^{log_3(x)} = 3^{2log_3(x)} = 3^{log_3(x^2)} = x^2$

3. Thank you so much. I just have a last question, the book is asking for a quadratic function $\displaystyle h(x)=ax^2+bx+c$. In this case, will $\displaystyle x^2$ be considered a quadratic function?

4. Yes, x^2 is a quadratic function, it just happens that b = c = 0. It's unsual though

5. Thank you again!