What is 2/3 log_{3}(2x-5)-5log_{3}(4x+2) ?

The solution to 2/3 log_{3}(2x-5)-5log_{3}(4x+2) is log_{3}(((2x-5)^{2/3})/((4x+2)^5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2/3 log_{3}(2x-5)-5log_{3}(4x+2)

simplify

\frac{2}{3} lo g_{3} (2 x - 5) - 5 lo g_{3} (4 x + 2)

lo g_{3} (\frac{( 2 x - 5 ) ^{\frac{2}{3}}}{( 4 x + 2 ) ^{5}})

Solution steps

\frac{2}{3} lo g_{3} (2 x - 5) - 5 lo g_{3} (4 x + 2)

Apply log rule:

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

\frac{2}{3} lo g_{3} (2 x - 5) = lo g_{3} ((2 x - 5)^{\frac{2}{3}})

= lo g_{3} ((2 x - 5)^{\frac{2}{3}}) - 5 lo g_{3} (4 x + 2)

Apply log rule:

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

5 lo g_{3} (4 x + 2) = lo g_{3} ((4 x + 2)^{5})

= lo g_{3} ((2 x - 5)^{\frac{2}{3}}) - lo g_{3} ((4 x + 2)^{5})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{3} ((2 x - 5)^{\frac{2}{3}}) - lo g_{3} ((4 x + 2)^{5}) = lo g_{3} (\frac{( 2 x - 5 ) ^{\frac{2}{3}}}{( 4 x + 2 ) ^{5}})

= lo g_{3} (\frac{( 2 x - 5 ) ^{\frac{2}{3}}}{( 4 x + 2 ) ^{5}})

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

ln (x^{5}) - ln (x^{3})

- 5 [lo g_{10} (x) - lo g_{10} (y - 2)]

4 lo g_{3} (x) + lo g_{3} (7)

ln (413.93) - ln (280)

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