Logarithm problems

[Jouster]

Homework Statement

By changing the base of log[SUB]3a[/SUB]9, express (log3a9)(1+loga3) as a single logarithm to base a. I don't know what to do to simplify the equation further

Relevant Equations

Logarithms

 

[renormalize]

I don't know what to do to simplify the equation further

Minimize your algebra by applying what you know about logarithms to finish rewriting your first line:
$$\log_{3a}9=\frac{\log_{a}9}{\log_{a}3a}=\frac{\log_{a}3^{2}}{\log_{a}a+\log_{a}3}=\frac{2\log_{a}3}{1+\log_{a}3}$$

 

[pasmith]

@Jouster: this is the latest of several threads you've started about logarithms where you have not applied the fundamental principle of logarithms: $\log_a(bc) = \log_a(b) + \log_a(c)$. You need to get into the habit of applying this principle before asking for help.

 

[berkeman]

Also @Jouster -- Please post your math using LaTeX, not in images. See the "LaTeX Guide" link below the Edit window for more information. Thank you.