If
$\displaystyle
3^{a} = 4^{b} = 36$
Find
(2/a) + (1/b).
I'm studying for a test, and I don't understand this problem at all. Thanks for the help!
$\displaystyle 3^{a}=36 \iff a=\frac{\ln(36)}{\ln(3)} $
$\displaystyle 4^{b}=36 \iff b=\frac{\ln(36)}{\ln(4)} $
$\displaystyle \frac{2}{\frac{\ln(36)}{\ln(3)}}+\frac{1}{\frac{\l n(36)}{\ln(4)}}=\frac{2\ln(3)}{\ln(36)}+\frac{\ln( 4)}{\ln(36)}$
$\displaystyle =\frac{2\ln(3)+\ln(4)}{\ln(36)}=\frac{\ln(9)+\ln(4 )}{\ln(36)}=\frac{\ln(36)}{\ln(36)}=1$