Question

solve for x. ln x = 4, e^x = 3

Solution

VerifiedStep 1

1 of 2Taking the natural logarithm of both sides, the given equation, $e^x=3 ,$ is equivalent to

$\begin{align*} \ln e^x&=\ln3 .\end{align*}$

Using the properties of logarithms, the equation above is equivalent to

$\begin{align*} x\ln e&=\ln3 &\text{(use Power Rule)} \\ x(1)&=\ln3 &(\ln e=1) \\ x&=\ln3 .\end{align*}$

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