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)

Solution

simplify

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

Solution

- 1 + lo g_{4} (x)

Solution steps

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Popular Examples

simplify 2log_{5}(t)+5log_{5}(t-6)+log_{5}(3t+7)simplify

2 lo g_{5} (t) + 5 lo g_{5} (t - 6) + lo g_{5} (3 t + 7)

simplify 1/2 ln(x)-1/2 ln(y)simplify

\frac{1}{2} ln (x) - \frac{1}{2} ln (y)

simplify log_{10}(x)-log_{10}(5)simplify

lo g_{10} (x) - lo g_{10} (5)

simplify log_{10}((x^2-9)/(x-3))simplify

lo g_{10} (\frac{x ^{2} - 9}{x - 3})

simplify ln(11x)-(5ln(x)+4ln(3y))simplify

ln (11 x) - (5 ln (x) + 4 ln (3 y))

Frequently Asked Questions (FAQ)

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