en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{4}(40)-log_{4}(5)

Solution

simplify

lo g_{4} (40) - lo g_{4} (5)

Solution

\frac{3}{2}

+1

Decimal Notation

1.5

Solution steps

lo g_{4} (40) - lo g_{4} (5)

Apply log rule:

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

lo g_{4} (40) - lo g_{4} (5) = lo g_{4} (\frac{40}{5})

= lo g_{4} (\frac{40}{5})

Factor the number:

4 = 2^{2}

= lo g_{2^{2}} (\frac{40}{5})

Apply log rule:

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

lo g_{2^{2}} (\frac{40}{5}) = \frac{1}{2} lo g_{2} (\frac{40}{5})

= \frac{1}{2} lo g_{2} (\frac{40}{5})

\frac{40}{5} = 2^{3}

= \frac{1}{2} lo g_{2} (2^{3})

Apply log rule:

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

lo g_{2} (2^{3}) = 3

= \frac{1}{2} \cdot 3

\frac{1}{2} \cdot 3 = \frac{3}{2}

= \frac{3}{2}

Popular Examples

(2x-4)/7 =(x-1)/5

\frac{2 x - 4}{7} = \frac{x - 1}{5}

factor 9m^2-16 factor

9 m^{2} - 16

x^{3} < 64 x

6 x - 3 = 21

simplify \sqrt[7]{36^{14}}simplify

Frequently Asked Questions (FAQ)

What is log_{4}(40)-log_{4}(5) ?
The solution to log_{4}(40)-log_{4}(5) is 3/2