What is the answer to 3=log_{b}(125) ?

The answer to 3=log_{b}(125) is b=5

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3=log_{b}(125)

3 = lo g_{b} (125)

b = 5

Solution steps

3 = lo g_{b} (125)

Apply log rules

3 = \frac{1}{lo g _{125} ( b )}

Multiply both sides by

lo g_{125} (b)

3 lo g_{125} (b) = \frac{1}{lo g _{125} ( b )} lo g_{125} (b)

Simplify

3 lo g_{125} (b) = 1

Divide both sides by

3

lo g_{125} (b) = \frac{1}{3}

Apply log rules

b = 5

Verify Solutions:

b = 5

True

The solution is

b = 5

lo g_{\frac{1}{8}} (13 - x) = - 2

\frac{1}{3} lo g_{2} (x) + 5 = 7

x, ln (5 - 2 x) = - 9

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

lo g_{10} (x^{4}) = 2