What is the answer to log_{x}(81)=-4 ?

The answer to log_{x}(81)=-4 is x= 1/3

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log_{x}(81)=-4

lo g_{x} (81) = - 4

x = \frac{1}{3}

Decimal Notation

x = 0.33333 \dots

Solution steps

lo g_{x} (81) = - 4

Apply log rules

\frac{1}{lo g _{81} ( x )} = - 4

Multiply both sides by

lo g_{81} (x)

\frac{1}{lo g _{81} ( x )} lo g_{81} (x) = - 4 lo g_{81} (x)

Simplify

1 = - 4 lo g_{81} (x)

Switch sides

- 4 lo g_{81} (x) = 1

Divide both sides by

- 4

lo g_{81} (x) = - \frac{1}{4}

Apply log rules

x = \frac{1}{3}

Verify Solutions:

x = \frac{1}{3}

True

The solution is

x = \frac{1}{3}

2 = ln (x)

lo g_{x} (4) = \frac{1}{2}

2 lo g_{2} (x) - lo g_{2} (x + 3) = 2

ln (x^{2}) = 18

lo g_{4} (x) = 5