Answer
(a) $x \approx -0.460517$
(b) $x\approx -0.602060$
Work Step by Step
(a)
Take the natural logarithm of both sides to obtain:
$\ln{e^{-5x}} = \ln{10}$
Use the rule $\ln{e^n} = n$ to obtain:
$-5x = \ln{10}
\\\dfrac{-5x}{-5}=\dfrac{\ln{10}}{-5}
\\x=\dfrac{\ln{10}}{-5}$
Use the rule $\log{(a^n)} = n\log{a}$ to obtain:
$x \approx -0.460517$
(b) Use a calculator to evaluate the answer and have:
$x =-2(0.3010299957)
\\x\approx -0.602060$
