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

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

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4=log_{b}(256)

4 = lo g_{b} (256)

b = 4

Solution steps

4 = lo g_{b} (256)

Apply log rules

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

Multiply both sides by

lo g_{256} (b)

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

Simplify

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_{3} (a) = - 2

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

lo g_{8} (x) = 3^{- 1}

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

395 = 113 lo g_{10} (0.1 x) + 78