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

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

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8=log_{b}(256)

8 = lo g_{b} (256)

b = 2

Solution steps

8 = lo g_{b} (256)

Apply log rules

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

Multiply both sides by

lo g_{256} (b)

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

Simplify

8 lo g_{256} (b) = 1

Divide both sides by

8

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

Apply log rules

b = 2

Verify Solutions:

b = 2

True

The solution is

b = 2

lo g_{10} (x) = 0.49

5 lo g_{10} (4 x) - 4.5 = 5.5

ln (\frac{t}{t - 1}) = 2

lo g_{2} (x^{2} + 6 x) = 4

ln (\frac{x}{x - 2}) = 1