What is simplify-3ln(x)+5/2 ln(x^2+x+6) ?

The solution to simplify-3ln(x)+5/2 ln(x^2+x+6) is ln(((x^2+x+6)^{5/2})/(x^3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-3ln(x)+5/2 ln(x^2+x+6)

simplify

- 3 ln (x) + \frac{5}{2} ln (x^{2} + x + 6)

ln \frac{( x ^{2} + x + 6 ) ^{\frac{5}{2}}}{x ^{3}}

Solution steps

- 3 ln (x) + \frac{5}{2} ln (x^{2} + x + 6)

Apply log rule:

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

3 ln (x) = ln (x^{3})

= - ln (x^{3}) + \frac{5}{2} ln (x^{2} + x + 6)

Apply log rule:

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

\frac{5}{2} ln (x^{2} + x + 6) = ln ((x^{2} + x + 6)^{\frac{5}{2}})

= - ln (x^{3}) + ln ((x^{2} + x + 6)^{\frac{5}{2}})

Apply log rule:

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

ln ((x^{2} + x + 6)^{\frac{5}{2}}) - ln (x^{3}) = ln \frac{( x ^{2} + x + 6 ) ^{\frac{5}{2}}}{x ^{3}}

= ln \frac{( x ^{2} + x + 6 ) ^{\frac{5}{2}}}{x ^{3}}

lo g_{3} (\frac{1}{x ^{2} y 3 ^{z}})

ln (\frac{273}{259})

4 lo g_{b} (y) + 3 lo g_{b} (x)

2 ln (x) - 4 ln (\frac{1}{y}) - 3 ln (x y)

- 3 ln (2) + ln (3) + 3

What is simplify-3ln(x)+5/2 ln(x^2+x+6) ?
The solution to simplify-3ln(x)+5/2 ln(x^2+x+6) is ln(((x^2+x+6)^{5/2})/(x^3))