What is 3ln(x+4)+9ln(x-4)-5ln(x) ?

The solution to 3ln(x+4)+9ln(x-4)-5ln(x) is ln(((x+4)^3(x-4)^9)/(x^5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3ln(x+4)+9ln(x-4)-5ln(x)

simplify

3 ln (x + 4) + 9 ln (x - 4) - 5 ln (x)

ln (\frac{( x + 4 ) ^{3} ( x - 4 ) ^{9}}{x ^{5}})

Solution steps

3 ln (x + 4) + 9 ln (x - 4) - 5 ln (x)

Apply log rule:

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

3 ln (x + 4) = ln ((x + 4)^{3})

= ln ((x + 4)^{3}) + 9 ln (x - 4) - 5 ln (x)

Apply log rule:

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

9 ln (x - 4) = ln ((x - 4)^{9})

= ln ((x + 4)^{3}) + ln ((x - 4)^{9}) - 5 ln (x)

Apply log rule:

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

ln ((x + 4)^{3}) + ln ((x - 4)^{9}) = ln ((x - 4)^{9} (x + 4)^{3})

= ln ((x + 4)^{3} (x - 4)^{9}) - 5 ln (x)

Apply log rule:

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

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

= ln ((x + 4)^{3} (x - 4)^{9}) - ln (x^{5})

Apply log rule:

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

ln ((x + 4)^{3} (x - 4)^{9}) - ln (x^{5}) = ln (\frac{( x - 4 ) ^{9} ( x + 4 ) ^{3}}{x ^{5}})

= ln (\frac{( x + 4 ) ^{3} ( x - 4 ) ^{9}}{x ^{5}})

lo g_{4} (\frac{y}{5 z ^{2}})

- ln (y) - ln (x)

\frac{1}{3} ln (x + 8) + \frac{1}{2} ln (x - 1)

lo g_{a} (x) + lo g_{a} (y) - lo g_{a} (f)

What is 3ln(x+4)+9ln(x-4)-5ln(x) ?
The solution to 3ln(x+4)+9ln(x-4)-5ln(x) is ln(((x+4)^3(x-4)^9)/(x^5))