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

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

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log_{x}(256)=8

lo g_{x} (256) = 8

x = 2

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 = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

ln (x - 2) = 2 + 3 ln (2)

lo g_{2} (x + 3) = 3 - lo g_{2} (x + 5)

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

lo g_{3} (2 x - 1) - lo g_{3} (x - 4) = 2

0.456 = ln (x^{2})