# Math Help - Proving a log identity

1. ## Proving a log identity

Hey guys!

I need help proving this log identity:

2. $\frac{3}{\log_{2}a}-\frac{2}{\log_{4} a}$

Change the base of all

3. $\frac{3}{\frac{\log_{\frac{1}{2}}a}{\log_{\frac{1} {2}}2}}-\frac{2}{\frac{\log_{\frac{1}{2}}a}{\log_{\frac{1} {2}}4}}$

$=\frac{3 \log_{\frac{1}{2}}2}{\log_{\frac{1}{2}}a}-\frac{2 \log_{\frac{1}{2}}4}{\log_{\frac{1}{2}}a}$

$=\frac{ \log_{\frac{1}{2}}2^3 - \log_{\frac{1}{2}}2^4}{\log_{\frac{1}{2}}a}$

$=\frac{ \log_{\frac{1}{2}}{\frac{2^3}{2^4}}}{\log_{\frac{1 }{2}}a}$

$=\frac{ \log_{\frac{1}{2}}{\frac{1}{2}}}{\log_{\frac{1}{2} }a}$

$=\frac{ 1}{\log_{\frac{1}{2}}a}$

4. thanks alot !!!! really appreciate it i spent forever on that question.