What is the answer to ln(1/x)=-5 ?

The answer to ln(1/x)=-5 is x=e^5

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ln(1/x)=-5

ln (\frac{1}{x}) = - 5

x = e^{5}

Decimal Notation

x = 148.41315 \dots

Solution steps

ln (\frac{1}{x}) = - 5

Apply log rules

\frac{1}{x} = e^{- 5}

Multiply both sides by

x

\frac{1}{x} x = e^{- 5} x

Simplify

e^{- 5} x : \frac{1}{e ^{5}} x

1 = \frac{1}{e ^{5}} x

Solve

1 = \frac{1}{e ^{5}} x : x = e^{5}

x = e^{5}

Verify Solutions:

x = e^{5}

True

The solution is

x = e^{5}

lo g_{10} (9 x) = lo g_{3} (3 x)

lo g_{3} (z) = - 5

ln (lo g_{2} (a - 3)) = lo g_{3} (1)

2 lo g_{3} (y - 2) - lo g_{3} (y - 4) = 2

lo g_{16} (x) = - \frac{1}{2}