Question

Solve each equation for x by converting to exponential form. In part (b), give two forms for the answer: one involving e and the other a calculator approximation rounded to two decimal places.
(a) log5(x) = −2
(b) ln(x) = −2

Answer 1

(a)= 1/25
b) = 1/e^2

Answer 2

(a)\[\log_5(x) = -2 \Rightarrow 5^{\log_5(x)} = 5^{-2} \Rightarrow x = \frac{1}{25}\](b)
\[\log(x) = -2 \Rightarrow e^{\log(x)} = e^{-2} = \frac{1}{e^2} \approx 0.14.\]

Answer 3

In general use this to convert from log to exponential or vis versa
\[\log_{b}x = y \leftarrow \rightarrow x = b^{y} \]