What is ln((x^7sqrt(x^2+5))/((x+5)^7)) ?

The solution to ln((x^7sqrt(x^2+5))/((x+5)^7)) is 7ln(x)+ln(sqrt(x^2+5))-7ln(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^7sqrt(x^2+5))/((x+5)^7))

simplify

ln (\frac{x ^{7} x ^{2} + 5}{( x + 5 ) ^{7}})

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

Solution steps

ln (\frac{x ^{7} x ^{2} + 5}{( x + 5 ) ^{7}})

Apply log rule:

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

ln (\frac{x ^{7} x ^{2} + 5}{( x + 5 ) ^{7}}) = ln (x^{7} x^{2} + 5) - ln ((x + 5)^{7})

= ln (x^{7} x^{2} + 5) - ln ((x + 5)^{7})

Apply log rule:

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

ln ((x + 5)^{7}) = 7 ln (x + 5)

= ln (x^{7} x^{2} + 5) - 7 ln (x + 5)

Apply log rule:

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

ln (x^{7} x^{2} + 5) = ln (x^{7}) + ln (x^{2} + 5)

= ln (x^{7}) + ln (x^{2} + 5) - 7 ln (x + 5)

Apply log rule:

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

ln (x^{7}) = 7 ln (x)

= 7 ln (x) + ln (x^{2} + 5) - 7 ln (x + 5)

lo g_{2} (lo g_{3} (a) n t i lo g_{3} (8))

ln (\frac{x}{x + ln ( x )})

ln (\frac{e ^{5}}{5})

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

lo g_{10} (\frac{a b ^{3}}{c ^{2}})

What is ln((x^7sqrt(x^2+5))/((x+5)^7)) ?
The solution to ln((x^7sqrt(x^2+5))/((x+5)^7)) is 7ln(x)+ln(sqrt(x^2+5))-7ln(x+5)