What is ln((x^9sqrt(x^2+3))/((x+3)^6)) ?

The solution to ln((x^9sqrt(x^2+3))/((x+3)^6)) is 9ln(x)+ln(sqrt(x^2+3))-6ln(x+3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((x^9sqrt(x^2+3))/((x+3)^6))

simplify

ln (\frac{x ^{9} x ^{2} + 3}{( x + 3 ) ^{6}})

9 ln (x) + ln (x^{2} + 3) - 6 ln (x + 3)

Solution steps

ln (\frac{x ^{9} x ^{2} + 3}{( x + 3 ) ^{6}})

Apply log rule:

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

ln (\frac{x ^{9} x ^{2} + 3}{( x + 3 ) ^{6}}) = ln (x^{9} x^{2} + 3) - ln ((x + 3)^{6})

= ln (x^{9} x^{2} + 3) - ln ((x + 3)^{6})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x + 3)^{6}) = 6 ln (x + 3)

= ln (x^{9} x^{2} + 3) - 6 ln (x + 3)

Apply log rule:

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

ln (x^{9} x^{2} + 3) = ln (x^{9}) + ln (x^{2} + 3)

= ln (x^{9}) + ln (x^{2} + 3) - 6 ln (x + 3)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{9}) = 9 ln (x)

= 9 ln (x) + ln (x^{2} + 3) - 6 ln (x + 3)

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

\frac{1}{2} ln (x) + 6 ln (y) - 9 ln (z)

lo g_{10} (\frac{- 5 ^{7} 2 ^{5}}{- 1 0 ^{8}})

ln (3 e^{7 x^{2} - 13 x + 5})

lo g_{b} (u^{5} v^{2})

What is ln((x^9sqrt(x^2+3))/((x+3)^6)) ?
The solution to ln((x^9sqrt(x^2+3))/((x+3)^6)) is 9ln(x)+ln(sqrt(x^2+3))-6ln(x+3)