en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{5}((x^2)/(x^3))

Solution

simplify

lo g_{5} (\frac{x ^{2}}{x ^{3}})

Solution

- lo g_{5} (x)

Solution steps

lo g_{5} (\frac{x ^{2}}{x ^{3}})

Simplify

\frac{x ^{2}}{x ^{3}} : \frac{1}{x}

= lo g_{5} (\frac{1}{x})

Simplify

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

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

Apply log rule

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

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

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

Apply rule:

1 \cdot a = a

= - lo g_{5} (x)

Popular Examples

simplify 8log_{9}(x)+16log_{9}(y)simplify

8 lo g_{9} (x) + 16 lo g_{9} (y)

join 1039/2 log_{2}(1039)join

\frac{1039}{2} lo g_{2} (1039)

simplify ln(50)-ln(10)simplify

ln (50) - ln (10)

simplify ln(300/187)simplify

ln (\frac{300}{187})

simplify 3log_{b}(q)+6log_{b}(v)simplify

3 lo g_{b} (q) + 6 lo g_{b} (v)

Frequently Asked Questions (FAQ)

What is log_{5}((x^2)/(x^3)) ?
The solution to log_{5}((x^2)/(x^3)) is -log_{5}(x)