en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{4}(1/4 x^2)

Solution

simplify

lo g_{4} (\frac{1}{4} x^{2})

Solution

- 1 + lo g_{2} (x)

Solution steps

lo g_{4} (\frac{1}{4} x^{2})

\frac{1}{4} = 4^{- 1}

= lo g_{4} (4^{- 1} x^{2})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{4} (4^{- 1} x^{2}) = lo g_{4} (4^{- 1}) + lo g_{4} (x^{2})

= lo g_{4} (4^{- 1}) + lo g_{4} (x^{2})

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{4} (4^{- 1}) = - 1

= - 1 + lo g_{4} (x^{2})

Simplify

lo g_{4} (x^{2}) : lo g_{2} (x)

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

Popular Examples

join-1/3 ln(2)join

- \frac{1}{3} ln (2)

expand log_{2}((sqrt(x))/8)expand

lo g_{2} (\frac{x}{8})

simplify 3log_{e}(x)-4log_{e}(sqrt(y))simplify

3 lo g_{e} (x) - 4 lo g_{e} (y)

expand log_{2}((16)/y)expand

lo g_{2} (\frac{16}{y})

simplify-(18ln(2))/(3ln(2)-ln(5))simplify

- \frac{18 ln ( 2 )}{3 ln ( 2 ) - ln ( 5 )}

Frequently Asked Questions (FAQ)

What is log_{4}(1/4 x^2) ?
The solution to log_{4}(1/4 x^2) is -1+log_{2}(x)