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Question

Find the real solution to the logarithmic equation
ln(x)+ln(2)=3

A
no real solutions
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B
0.5×e3
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C
e3/ln(2)
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D
3e/2
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E
3ln(2)
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Solution

The correct option is B 0.5×e3
Let both sides be exponents of the base e.
The equation ln(x)+ln(2)=3
eln(x)+ln(2)=e3
eln(2x)=e3
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(2x)=e3
2x=e3
x=0.5×e3

Hence, option B is correct.

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