en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{5}(1/3)

Solution

simplify

lo g_{5} (\frac{1}{3})

Solution

- lo g_{5} (3)

+1

Decimal Notation

- 0.68260 \dots

Solution steps

lo g_{5} (\frac{1}{3})

\frac{1}{3} = 3^{- 1}

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{5} (3^{- 1}) = - 1 \cdot lo g_{5} (3)

= - 1 \cdot lo g_{5} (3)

Apply rule:

1 \cdot a = a

= - lo g_{5} (3)

Popular Examples

expand (3u+2v)^3 expand

(3 u + 2 v)^{3}

simplify (-3i)(10i)simplify

(- 3 i) (10 i)

simplify 3.14\times 9^2 simplify

3.14 \times 9^{2}

4 \frac{1}{2} \div 2

simplify (-2/7)^0 simplify

(- \frac{2}{7})^{0}

Frequently Asked Questions (FAQ)

What is log_{5}(1/3) ?
The solution to log_{5}(1/3) is -log_{5}(3)