Expert Answer to "How do you solve ln⁡x=2?"

Carla Murphy

Answered question

2021-12-13

How do you solve

\ln x = 2 ?

sirpsta3u

Beginner2021-12-14Added 42 answers

x = e^{2}

Explanation:
Base

e

cancels out with the natural log

(\ln)

function, so we can apply it to both sides. We get

e^{\ln x} = e^{2}

Notice base-

e

and

\ln

cancel, and were

Melissa Moore

Beginner2021-12-15Added 32 answers

\Rightarrow x = e^{2}

Explanation:

\Rightarrow \ln (x) = 2

Natural log has a base of

e

. More explicitly we can write:

\Rightarrow \ln_{e} (x) = 2

Logarithms have the following form:

\Rightarrow \log_{a} (x) = b

They also have the property:

\Rightarrow a^{\log_{a} (x)} = x

So we can raise both sides of our equation by

e

to extract the

x

\Rightarrow e^{\ln (x)} = e^{2}

\Rightarrow x = e^{2}

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