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Question

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

Solution

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

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

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

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

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