What is log_{2}(0.3) ?

The solution to log_{2}(0.3) is log_{2}(3)-1-log_{2}(5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{2}(0.3)

simplify

lo g_{2} (0.3)

lo g_{2} (3) - 1 - lo g_{2} (5)

Decimal Notation

- 1.73696 \dots

Solution steps

lo g_{2} (0.3)

0.3 = \frac{3}{10}

= lo g_{2} (\frac{3}{10})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{2} (\frac{3}{10}) = lo g_{2} (3) - lo g_{2} (10)

= lo g_{2} (3) - lo g_{2} (10)

lo g_{2} (10) = 1 + lo g_{2} (5)

= lo g_{2} (3) - (1 + lo g_{2} (5))

Apply the distributive law:

- (a + b) = - a - b

- (1 + lo g_{2} (5)) = - 1 - lo g_{2} (5)

= lo g_{2} (3) - 1 - lo g_{2} (5)

3^{2} \cdot 4^{2} \cdot 5^{2}

a^{l o g_{a} (b)}

x^{3} \cdot x^{- 5}

(- 1)^{2} + (- 3)^{2}

\frac{5}{6} m - \frac{7}{8} m