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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

log_{b}(125)=3

lo g_{b} (125) = 3

b = 5

Solution steps

lo g_{b} (125) = 3

Apply log rules

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

Multiply both sides by

lo g_{125} (b)

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

Simplify

1 = 3 lo g_{125} (b)

Switch sides

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

ln (x) - \frac{3}{ln ( x )} = - 2

lo g_{e} (x) = 0

lo g_{x} (\frac{1}{64}) = - 2

lo g_{2} (x + 4) = 3

lo g_{6} ((5 x - 9)^{2}) = 4