What is 5ln(x-2)-ln(x+2)-3ln(x) ?

The solution to 5ln(x-2)-ln(x+2)-3ln(x) is ln(((x-2)^5)/(x^3(x+2)))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 5ln(x-2)-ln(x+2)-3ln(x)

simplify

5 ln (x - 2) - ln (x + 2) - 3 ln (x)

ln (\frac{( x - 2 ) ^{5}}{x ^{3} ( x + 2 )})

Solution steps

5 ln (x - 2) - ln (x + 2) - 3 ln (x)

Apply log rule:

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

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

= ln ((x - 2)^{5}) - ln (x + 2) - 3 ln (x)

Apply log rule:

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

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

= ln (\frac{( x - 2 ) ^{5}}{x + 2}) - 3 ln (x)

Apply log rule:

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

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

= ln (\frac{( x - 2 ) ^{5}}{x + 2}) - ln (x^{3})

Apply log rule:

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

ln (\frac{( x - 2 ) ^{5}}{x + 2}) - ln (x^{3}) = ln (\frac{\frac{( x - 2 ) ^{5}}{x + 2}}{x ^{3}})

= ln (\frac{\frac{( x - 2 ) ^{5}}{x + 2}}{x ^{3}})

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= ln (\frac{( x - 2 ) ^{5}}{x ^{3} ( x + 2 )})

ln (7 e^{x})

lo g_{7} (32) - lo g_{7} (8)

ln (x) - ln (5)

lo g_{10} (\frac{R ^{5} S ^{4}}{Z ^{6}})

ln (\frac{1}{x + 1})

What is 5ln(x-2)-ln(x+2)-3ln(x) ?
The solution to 5ln(x-2)-ln(x+2)-3ln(x) is ln(((x-2)^5)/(x^3(x+2)))