What is the answer to log_{x}(256)=-8 ?

The answer to log_{x}(256)=-8 is x= 1/2

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log_{x}(256)=-8

lo g_{x} (256) = - 8

x = \frac{1}{2}

Decimal

x = 0.5

Solution steps

lo g_{x} (256) = - 8

Apply log rules

\frac{1}{lo g _{256} ( x )} = - 8

Multiply both sides by

lo g_{256} (x)

\frac{1}{lo g _{256} ( x )} lo g_{256} (x) = - 8 lo g_{256} (x)

Simplify

1 = - 8 lo g_{256} (x)

Switch sides

- 8 lo g_{256} (x) = 1

Divide both sides by

- 8

lo g_{256} (x) = - \frac{1}{8}

Apply log rules

x = \frac{1}{2}

Verify Solutions:

x = \frac{1}{2}

True

The solution is

x = \frac{1}{2}

lo g_{10} (x) - lo g_{10} (8) = 3

lo g_{10} (x + 12) = lo g_{10} (x) + lo g_{10} (12)

lo g_{3} (x) = - 5

0 = ln (x) + 1

lo g_{4} ((x - 2)^{2}) = - 3