en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{10}(1/(x^2))

Solution

simplify

lo g_{10} (\frac{1}{x ^{2}})

Solution

- 2 lo g_{10} (x)

Solution steps

lo g_{10} (\frac{1}{x ^{2}})

Simplify

\frac{1}{x ^{2}} : (x^{2})^{- 1}

= lo g_{10} ((x^{2})^{- 1})

Apply log rule

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

lo g_{10} ((x^{2})^{- 1}) = - 1 \cdot lo g_{10} (x^{2})

= - 1 \cdot lo g_{10} (x^{2})

Apply rule:

1 \cdot a = a

= - lo g_{10} (x^{2})

Apply log rule

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

- lo g_{10} (x^{2}) = - 2 lo g_{10} (x)

= - 2 lo g_{10} (x)

Popular Examples

simplify log_{9}(xsqrt(y))simplify

lo g_{9} (x y)

simplify ln(1/1000)simplify

ln (\frac{1}{1000})

simplify ln^2(1/2)simplify

ln^{2} (\frac{1}{2})

simplify ln(y)+ln(5)simplify

ln (y) + ln (5)

simplify log_{3}(9/(sqrt(x+7)))simplify

lo g_{3} (\frac{9}{x + 7})

Frequently Asked Questions (FAQ)

What is log_{10}(1/(x^2)) ?
The solution to log_{10}(1/(x^2)) is -2log_{10}(x)