en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{1/25}(5)

Solution

simplify

lo g_{\frac{1}{25}} (5)

Solution

- \frac{1}{2}

+1

Decimal Notation

- 0.5

Solution steps

lo g_{\frac{1}{25}} (5)

Apply log rule:

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

lo g_{\frac{1}{25}} (5) = - lo g_{25} (5)

= - lo g_{25} (5)

Factor the number:

25 = 5^{2}

= - lo g_{5^{2}} (5)

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{5^{2}} (5) = \frac{1}{2} lo g_{5} (5)

= - \frac{1}{2} lo g_{5} (5)

Apply log rule:

lo g_{a} (a) = 1

lo g_{5} (5) = 1

= - \frac{1}{2} \cdot 1

Multiply the numbers:

\frac{1}{2} \cdot 1 = \frac{1}{2}

= - \frac{1}{2}

Popular Examples

simplify x^3-1/(x^3)simplify

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

- 8 \frac{3}{16}

factor-5x-5 factor

- 5 x - 5

simplify (-50)/(-10)simplify

\frac{- 50}{- 10}

simplify-log_{2}(1/4)simplify

- lo g_{2} (\frac{1}{4})

Frequently Asked Questions (FAQ)

What is log_{1/25}(5) ?
The solution to log_{1/25}(5) is -1/2