What is ln((x^9sqrt(x^2+5))/((x+5)^6)) ?

The solution to ln((x^9sqrt(x^2+5))/((x+5)^6)) is 9ln(x)+ln(sqrt(x^2+5))-6ln(x+5)

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+5))/((x+5)^6))

simplify

ln (\frac{x ^{9} x ^{2} + 5}{( x + 5 ) ^{6}})

9 ln (x) + ln (x^{2} + 5) - 6 ln (x + 5)

Solution steps

ln (\frac{x ^{9} x ^{2} + 5}{( x + 5 ) ^{6}})

Apply log rule:

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

ln (\frac{x ^{9} x ^{2} + 5}{( x + 5 ) ^{6}}) = ln (x^{9} x^{2} + 5) - ln ((x + 5)^{6})

= ln (x^{9} x^{2} + 5) - ln ((x + 5)^{6})

Apply log rule:

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

ln ((x + 5)^{6}) = 6 ln (x + 5)

= ln (x^{9} x^{2} + 5) - 6 ln (x + 5)

Apply log rule:

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

ln (x^{9} x^{2} + 5) = ln (x^{9}) + ln (x^{2} + 5)

= ln (x^{9}) + ln (x^{2} + 5) - 6 ln (x + 5)

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} + 5) - 6 ln (x + 5)

ln (\frac{0.01}{( 1 - 0.01 )})

ln (2 x^{4})

ln (\frac{e ^{4}}{t})

\frac{1}{5} \cdot lo g_{2} (5)

ln (\frac{6.1 \cdot 5.05}{9.42 \cdot 1 0 ^{- 3}})

What is ln((x^9sqrt(x^2+5))/((x+5)^6)) ?
The solution to ln((x^9sqrt(x^2+5))/((x+5)^6)) is 9ln(x)+ln(sqrt(x^2+5))-6ln(x+5)