Question

Find a formula for (f(g(x)) assuming f(x)=3^(3+7x) and g(x)=log3 (x). I have tried it so many times but can't get the correct answer!

Answer 1

\[f(x)=3^{3+7x}\\
g(x)=\log_3x\]
\[\large f(g(x))=f(\log_3x)=3^{3+7\log_3x}=3^3\cdot3^{7\log_3x}\]
Use the following properties:
\[a\log_bx=\log_b(x^a)\\
b^{\log_bx}=x\]

Answer 2

Thank you so much! Is that the simplest form it can be in?

Answer 3

Have you applied the properties yet?

Answer 4

I got it down to 27(3^log3x)^7 so 27x^7. Correct?

Answer 5

Yes

Answer 6

Sweet! Thank you for your help!