Answer
(a) $10^{\log36}=36$
(b) $\ln{e^3}=3$
(c) $\log_3\sqrt{27}=\frac{2}{3}$
(d) $\log_280-\log_210=3$
(e) $\log_84=\frac{3}{2}$
(f) $\log_64+log_69=2$
Work Step by Step
A few remainder:
$\log_mm^n=n$
$\log_ma-\log_mb=\frac{\log_ma}{\log_mb}$
$\log_ma+\log_mb=\log_m(a\times b)$
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(a) $10^{\log36}=36^{\log10}=36^1=36$
Note, $\log{m}$ stands for logarithm with base $10$. Base $10$ is often omitted.
(b) $\ln{e^3}=3$
$ln$ stands for logarithm with base $e$
(c) $\log_3\sqrt{27}=\log_33^{\frac{2}{3}}=\frac{2}{3}$
(d) $\log_280-\log_210=\log_2\frac{80}{10}=\log_28=\log_22^3=3$
(e) $\log_84=\log_88^{\frac{3}{2}}=\frac{3}{2}$
(f) $\log_64+log_69=\log_6(4\times9)=\log_636=\log_66^2=2$