What is the answer to log_{x}(2)= 1/3 ?

The answer to log_{x}(2)= 1/3 is x=8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

log_{x}(2)= 1/3

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

x = 8

Solution steps

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

Apply log rules

\frac{1}{lo g _{2} ( x )} = \frac{1}{3}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot 3 = lo g_{2} (x) \cdot 1

Simplify

3 = lo g_{2} (x)

Apply log rules

8 = x

Switch sides

x = 8

Verify Solutions:

x = 8

True

The solution is

x = 8

lo g_{4} (- 3 x + 7) = 1

lo g_{6} (x - 8) = 2 - lo g_{6} (x + 8)

lo g_{10} (lo g_{10} (x)) = 1

lo g_{3} (8 x + 9) = 4

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