What is the answer to log_{x}(256)=-4 ?

The answer to log_{x}(256)=-4 is x= 1/4

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log_{x}(256)=-4

lo g_{x} (256) = - 4

x = \frac{1}{4}

Decimal Notation

x = 0.25

Solution steps

lo g_{x} (256) = - 4

Apply log rules

\frac{1}{lo g _{256} ( x )} = - 4

Multiply both sides by

lo g_{256} (x)

\frac{1}{lo g _{256} ( x )} lo g_{256} (x) = - 4 lo g_{256} (x)

Simplify

1 = - 4 lo g_{256} (x)

Switch sides

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

Divide both sides by

- 4

lo g_{256} (x) = - \frac{1}{4}

Apply log rules

x = \frac{1}{4}

Verify Solutions:

x = \frac{1}{4}

True

The solution is

x = \frac{1}{4}

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lo g_{2} (x + 5) = 5

lo g_{5} (x + 12) - lo g_{5} (x + 2) = 1

6 ln (7 x + 6) - 14 = 10