What is the answer to ln(1/x)=-2 ?

The answer to ln(1/x)=-2 is x=e^2

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ln(1/x)=-2

ln (\frac{1}{x}) = - 2

x = e^{2}

Decimal

x = 7.38905 \dots

Solution steps

ln (\frac{1}{x}) = - 2

Apply log rules

\frac{1}{x} = e^{- 2}

Multiply both sides by

x

\frac{1}{x} x = e^{- 2} x

Simplify

e^{- 2} x : \frac{1}{e ^{2}} x

1 = \frac{1}{e ^{2}} x

Solve

1 = \frac{1}{e ^{2}} x : x = e^{2}

x = e^{2}

Verify Solutions:

x = e^{2}

True

The solution is

x = e^{2}

a, lo g_{ab} (b) = 15

lo g_{10} (x) + lo g_{10} (2) = 1

lo g_{10} (3 x + 1) = 5

59.61 = 29.58 ln (\frac{1 0 ^{- 6}}{x \cdot 3})

y, ln (y) = x + ln (x - 1) + c