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

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

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ln(1/x)=5

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

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

Decimal Notation

x = 0.00673 \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

1 = e^{5} x

Solve

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

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

Verify Solutions:

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

True

The solution is

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

0 = lo g_{10} (x^{20})

(ln (x))^{2} = ln^{2} (x)

ln (1 + x^{2}) = 0

lo g_{x + 1} (25) = 2

lo g_{2} (2 x - 10) = 5