What is 7ln(x)-ln(x^2-4)+ln(x^2+2x) ?

The solution to 7ln(x)-ln(x^2-4)+ln(x^2+2x) is ln((x^8)/(x-2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 7ln(x)-ln(x^2-4)+ln(x^2+2x)

simplify

7 ln (x) - ln (x^{2} - 4) + ln (x^{2} + 2 x)

ln (\frac{x ^{8}}{x - 2})

Solution steps

7 ln (x) - ln (x^{2} - 4) + ln (x^{2} + 2 x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (x^{7}) - ln (x^{2} - 4) + ln (x^{2} + 2 x)

Apply log rule:

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

ln (x^{7}) - ln (x^{2} - 4) = ln (\frac{x ^{7}}{x ^{2} - 4})

= ln (\frac{x ^{7}}{x ^{2} - 4}) + ln (x^{2} + 2 x)

Apply log rule:

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

ln (\frac{x ^{7}}{x ^{2} - 4}) + ln (x^{2} + 2 x) = ln (\frac{x ^{7}}{x ^{2} - 4} (x^{2} + 2 x))

= ln (\frac{x ^{7}}{x ^{2} - 4} (x^{2} + 2 x))

Simplify

\frac{x ^{7}}{x ^{2} - 4} (x^{2} + 2 x) : \frac{x ^{8}}{x - 2}

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

3 lo g_{5} (2) + lo g_{5} (7)

\frac{1}{2} lo g_{2} (5) - 2 lo g_{2} (3)

\frac{1}{2} lo g_{2} (5) - 2 lo g_{2} (6)

lo g_{10} (\frac{x y}{z})

lo g_{10} (y) + 4 lo g_{10} (z)

What is 7ln(x)-ln(x^2-4)+ln(x^2+2x) ?
The solution to 7ln(x)-ln(x^2-4)+ln(x^2+2x) is ln((x^8)/(x-2))