What is ln(x-1)+2ln(x+4)-3ln(x-5) ?

The solution to ln(x-1)+2ln(x+4)-3ln(x-5) is ln(((x-1)(x+4)^2)/((x-5)^3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(x-1)+2ln(x+4)-3ln(x-5)

simplify

ln (x - 1) + 2 ln (x + 4) - 3 ln (x - 5)

ln (\frac{( x - 1 ) ( x + 4 ) ^{2}}{( x - 5 ) ^{3}})

Solution steps

ln (x - 1) + 2 ln (x + 4) - 3 ln (x - 5)

Apply log rule:

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

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

= ln (x - 1) + ln ((x + 4)^{2}) - 3 ln (x - 5)

Apply log rule:

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

ln (x - 1) + ln ((x + 4)^{2}) = ln ((x + 4)^{2} (x - 1))

= ln ((x - 1) (x + 4)^{2}) - 3 ln (x - 5)

Apply log rule:

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

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

= ln ((x - 1) (x + 4)^{2}) - ln ((x - 5)^{3})

Apply log rule:

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

ln ((x - 1) (x + 4)^{2}) - ln ((x - 5)^{3}) = ln (\frac{( x + 4 ) ^{2} ( x - 1 )}{( x - 5 ) ^{3}})

= ln (\frac{( x - 1 ) ( x + 4 ) ^{2}}{( x - 5 ) ^{3}})

ln (x^{2} + 3) + 2 ln (x) + C

3 lo g_{b} (y) + 7 lo g_{b} (z)

ln (\frac{1}{23})

9 \cdot ln (8) - ln (2!) + 7 \cdot ln (2) - ln (7!) - 3 \cdot 8

3 lo g_{b} (z) + 2 (lo g_{b} (y) - 5 lo g_{b} (x))

What is ln(x-1)+2ln(x+4)-3ln(x-5) ?
The solution to ln(x-1)+2ln(x+4)-3ln(x-5) is ln(((x-1)(x+4)^2)/((x-5)^3))