What is the answer to log_{a}(64)=-2 ?

The answer to log_{a}(64)=-2 is a= 1/8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

log_{a}(64)=-2

lo g_{a} (64) = - 2

a = \frac{1}{8}

Decimal Notation

a = 0.125

Solution steps

lo g_{a} (64) = - 2

Apply log rules

\frac{1}{lo g _{64} ( a )} = - 2

Multiply both sides by

lo g_{64} (a)

\frac{1}{lo g _{64} ( a )} lo g_{64} (a) = - 2 lo g_{64} (a)

Simplify

1 = - 2 lo g_{64} (a)

Switch sides

- 2 lo g_{64} (a) = 1

Divide both sides by

- 2

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

Apply log rules

a = \frac{1}{8}

Verify Solutions:

a = \frac{1}{8}

True

The solution is

a = \frac{1}{8}

x + lo g_{10} (x + 4) = 6

lo g_{2} (9 x + 12) - lo g_{2} (3) = 4

3 = lo g_{10} (p (x)) (24 x - 18 x^{2})

ln (x - 2) = 0.5

lo g_{4} (x + 5) + lo g_{4} (3 x - 7) = 2