What is ln((x^6sqrt(x^2+7))/((x+7)^2)) ?

The solution to ln((x^6sqrt(x^2+7))/((x+7)^2)) is 6ln(x)+ln(sqrt(x^2+7))-2ln(x+7)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((x^6sqrt(x^2+7))/((x+7)^2))

simplify

ln (\frac{x ^{6} x ^{2} + 7}{( x + 7 ) ^{2}})

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

Solution steps

ln (\frac{x ^{6} x ^{2} + 7}{( x + 7 ) ^{2}})

Apply log rule:

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

ln (\frac{x ^{6} x ^{2} + 7}{( x + 7 ) ^{2}}) = ln (x^{6} x^{2} + 7) - ln ((x + 7)^{2})

= ln (x^{6} x^{2} + 7) - ln ((x + 7)^{2})

Apply log rule:

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

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

= ln (x^{6} x^{2} + 7) - 2 ln (x + 7)

Apply log rule:

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

ln (x^{6} x^{2} + 7) = ln (x^{6}) + ln (x^{2} + 7)

= ln (x^{6}) + ln (x^{2} + 7) - 2 ln (x + 7)

Apply log rule:

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

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

= 6 ln (x) + ln (x^{2} + 7) - 2 ln (x + 7)

lo g_{3} (\frac{2 x}{x + 1})

2 (lo g_{2} (393) - lo g_{2} (7))

ln (6 x^{2})

- lo g_{10} (- 0.83 x 1 0^{14})

lo g_{6} (A B^{2})

What is ln((x^6sqrt(x^2+7))/((x+7)^2)) ?
The solution to ln((x^6sqrt(x^2+7))/((x+7)^2)) is 6ln(x)+ln(sqrt(x^2+7))-2ln(x+7)