Answer
(a) $x = -2\cdot \log{2}$
(b) $x\approx -0.602060$
Work Step by Step
(a)
Take the common logarithm of both sides to obtain:
$\log{10^{-x}} = \log{4}$
Use the rule $\log{10^n} = n$ to obtain:
$-x = \log{4}
\\-x=\log{(2^2)}
\\-1(-x) = -1(\log{(2^2)}
\\x = -\log{(2^2)}$
Use the rule $\log{(a^n)} = n\log{a}$ to obtain:
$x = -2\cdot \log{2}$
(b) Use a calculator to evaluate the answer and have:
$x =-2(0.3010299957)
\\x\approx -0.602060$