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

The answer to log_{b}(256)=4 is b=4

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log_{b}(256)=4

lo g_{b} (256) = 4

b = 4

Solution steps

lo g_{b} (256) = 4

Apply log rules

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

Multiply both sides by

lo g_{256} (b)

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

Simplify

1 = 4 lo g_{256} (b)

Switch sides

4 lo g_{256} (b) = 1

Divide both sides by

4

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

Apply log rules

b = 4

Verify Solutions:

b = 4

True

The solution is

b = 4

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

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

400 = 300 lo g_{10} (d) + 65

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

lo g_{3} (x + 7) - lo g_{3} (x - 7) = 2