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Question

Find all the real solutions to the logarithmic equation
ln(x)=2

A
2
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B
2e
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C
1,0
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D
no real solutions
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E
e2
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Solution

The correct option is E e2
Let both sides be exponents of the base e. The equation ln(x)=2 can be rewritten as eln(x)=e2.

By now you should know that when the base of the exponent and the base of the logarithm are the same, the left side can be written x. The equation eln(x)=e2 can now be written as x=e2.

Therefore, x=e2.

Hence option E is correct.

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