What is ln((x^8sqrt(x^2+6))/((x+6)^3)) ?

The solution to ln((x^8sqrt(x^2+6))/((x+6)^3)) is 8ln(x)+ln(sqrt(x^2+6))-3ln(x+6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((x^8sqrt(x^2+6))/((x+6)^3))

simplify

ln (\frac{x ^{8} x ^{2} + 6}{( x + 6 ) ^{3}})

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

Solution steps

ln (\frac{x ^{8} x ^{2} + 6}{( x + 6 ) ^{3}})

Apply log rule:

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

ln (\frac{x ^{8} x ^{2} + 6}{( x + 6 ) ^{3}}) = ln (x^{8} x^{2} + 6) - ln ((x + 6)^{3})

= ln (x^{8} x^{2} + 6) - ln ((x + 6)^{3})

Apply log rule:

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

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

= ln (x^{8} x^{2} + 6) - 3 ln (x + 6)

Apply log rule:

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

ln (x^{8} x^{2} + 6) = ln (x^{8}) + ln (x^{2} + 6)

= ln (x^{8}) + ln (x^{2} + 6) - 3 ln (x + 6)

Apply log rule:

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

ln (x^{8}) = 8 ln (x)

= 8 ln (x) + ln (x^{2} + 6) - 3 ln (x + 6)

ln (\frac{27}{4}) - 1

x^{2} - \frac{13}{6} ln ∣ x + 2 ∣ + \frac{19}{6} ln ∣ x - 4 ∣ + 4

9 \cdot ln (3) - ln (2!) + 7 \cdot ln (2) - ln (7!) - 3 \cdot 3

ln (a + b) + 4 ln (a - b) - 5 ln (C)

12 lo g_{10} (x) + 5 lo g_{10} (y)

What is ln((x^8sqrt(x^2+6))/((x+6)^3)) ?
The solution to ln((x^8sqrt(x^2+6))/((x+6)^3)) is 8ln(x)+ln(sqrt(x^2+6))-3ln(x+6)