Question

rewrite each equation in logarithmic form: (a) $e^x = 47$ (b) $e^{90} = x$

Explanation:

Step1: Use natural log definition

For $e^x = 47$, apply $\ln(e^a)=a$.
$\ln(e^x) = \ln(47)$

Step2: Simplify left side

$x = \ln(47)$

Step3: Use natural log definition

For $e^{90} = x$, apply $\ln(e^a)=a$.
$\ln(e^{90}) = \ln(x)$

Step4: Simplify left side

$90 = \ln(x)$

Answer:

(a) $\ln(47) = x$
(b) $\ln(x) = 90$