Answer
(a) $log_{a}\frac{1}{a} =-1$
(b) $10^{(log_{10}4+log_{10}7)} =28$
Work Step by Step
(a) Use logarithmic base formulas $\log_{b}x=\frac{log x}{log b}$ and $\log b^{x}=x log b$
$log_{a}\frac{1}{a}=log_{a}a^{-1}$
$=-1 log_{a}a$
$=-1\times\frac{log a}{log a}$
$=-1$
Hence, $log_{a}\frac{1}{a} =-1$
(b) $10^{(log_{10}4+log_{10}7)}= 10^{log_{10}(4\times7)}$
$=10^{log_{10}(28)}$
Apply $\log b^{\log_{b}x}=x$
Hence, $10^{(log_{10}4+log_{10}7)} =28$
