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Convert the natural logs to exponential form, and solve. If 1n e^-3 = x then x = ?

Convert the natural logs to exponential form, and solve. If 1n e^-3 = x then x = ?-example-1
User Ychaouche
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The natural logarithm of a number is defined as follows:


\ln A=x_{}

means that when we elevate the Euler number e to x, the result is A:


\ln A=x\Rightarrow A=e^x

In this problem, we have


A=e^(-3)

Thus


\ln e^(-3)=x\Rightarrow e^(-3)=e^x

Then, since the bases are the same, for the equation to hold we need the exponents to be the same:


\begin{gathered} e^(-3)=e^x\Rightarrow-3=x \\ \\ \therefore x=-3 \end{gathered}

User Jdphenix
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