What is the answer to log_{a}(1/16)=2 ?

The answer to log_{a}(1/16)=2 is a= 1/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

log_{a}(1/16)=2

lo g_{a} (\frac{1}{16}) = 2

a = \frac{1}{4}

Decimal

a = 0.25

Solution steps

lo g_{a} (\frac{1}{16}) = 2

Apply log rules

\frac{ln ( \frac{1}{16} )}{ln ( a )} = 2

Multiply both sides by

ln (a)

\frac{ln ( \frac{1}{16} )}{ln ( a )} ln (a) = 2 ln (a)

Apply log rules

a = \frac{1}{4}

Verify Solutions:

a = \frac{1}{4}

True

The solution is

a = \frac{1}{4}

lo g_{3} (x^{2}) = 1

ln (\frac{760}{x}) = 0.002192398

lo g_{5} (3 x^{2} + 6 x - 20) = 2

lo g_{10} (x) = 5 x

lo g_{10} (x) = - 5