What is simplify-2/3 log_{b}(x+1)-1/4 log_{b}(x+2) ?

The solution to simplify-2/3 log_{b}(x+1)-1/4 log_{b}(x+2) is -log_{b}((x+1)^{2/3}(x+2)^{1/4})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-2/3 log_{b}(x+1)-1/4 log_{b}(x+2)

simplify

- \frac{2}{3} lo g_{b} (x + 1) - \frac{1}{4} lo g_{b} (x + 2)

- lo g_{b} ((x + 1)^{\frac{2}{3}} (x + 2)^{\frac{1}{4}})

Solution steps

- \frac{2}{3} lo g_{b} (x + 1) - \frac{1}{4} lo g_{b} (x + 2)

Apply log rule:

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

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

= - lo g_{b} ((x + 1)^{\frac{2}{3}}) - \frac{1}{4} lo g_{b} (x + 2)

Apply log rule:

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

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

= - lo g_{b} ((x + 1)^{\frac{2}{3}}) - lo g_{b} ((x + 2)^{\frac{1}{4}})

Rewrite

- lo g_{b} ((x + 1)^{\frac{2}{3}}) - lo g_{b} ((x + 2)^{\frac{1}{4}})

- (lo g_{b} ((x + 1)^{\frac{2}{3}}) + lo g_{b} ((x + 2)^{\frac{1}{4}}))

= - (lo g_{b} ((x + 1)^{\frac{2}{3}}) + lo g_{b} ((x + 2)^{\frac{1}{4}}))

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{b} ((x + 1)^{\frac{2}{3}}) + lo g_{b} ((x + 2)^{\frac{1}{4}}) = lo g_{b} ((x + 1)^{\frac{2}{3}} (x + 2)^{\frac{1}{4}})

= - lo g_{b} ((x + 1)^{\frac{2}{3}} (x + 2)^{\frac{1}{4}})

ln (\frac{e ^{8 x} + 1}{e ^{- 3 x} + 1})

- \frac{6}{9} lo g_{2} (\frac{6}{9}) - \frac{3}{9} lo g_{2} (\frac{3}{9})

4 lo g_{b} (2) + lo g_{b} (5)

lo g_{7} (2) + lo g_{7} (5)

ln (\frac{8}{5 x ^{5} y})

What is simplify-2/3 log_{b}(x+1)-1/4 log_{b}(x+2) ?
The solution to simplify-2/3 log_{b}(x+1)-1/4 log_{b}(x+2) is -log_{b}((x+1)^{2/3}(x+2)^{1/4})