What is the answer to 3=log_{b}(512) ?

The answer to 3=log_{b}(512) is b=8

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3=log_{b}(512)

3 = lo g_{b} (512)

b = 8

Solution steps

3 = lo g_{b} (512)

Apply log rules

3 = \frac{1}{lo g _{512} ( b )}

Multiply both sides by

lo g_{512} (b)

3 lo g_{512} (b) = \frac{1}{lo g _{512} ( b )} lo g_{512} (b)

Simplify

3 lo g_{512} (b) = 1

Divide both sides by

3

lo g_{512} (b) = \frac{1}{3}

Apply log rules

b = 8

Verify Solutions:

b = 8

True

The solution is

b = 8

ln (e^{x} - 1) = ln (e^{- x} - 1)

ln (2 x) = e^{2}

lo g_{4} (10) + lo g_{4} (x + 9) = 4

0.56 = lo g_{10} (x)

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