What is ln(a+b)+3ln(a-b)-4ln(c) ?

The solution to ln(a+b)+3ln(a-b)-4ln(c) is ln(((a+b)(a-b)^3)/(c^4))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(a+b)+3ln(a-b)-4ln(c)

simplify

ln (a + b) + 3 ln (a - b) - 4 ln (c)

ln (\frac{( a + b ) ( a - b ) ^{3}}{c ^{4}})

Solution steps

ln (a + b) + 3 ln (a - b) - 4 ln (c)

Apply log rule:

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

3 ln (a - b) = ln ((a - b)^{3})

= ln (a + b) + ln ((a - b)^{3}) - 4 ln (c)

Apply log rule:

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

ln (a + b) + ln ((a - b)^{3}) = ln ((a - b)^{3} (a + b))

= ln ((a + b) (a - b)^{3}) - 4 ln (c)

Apply log rule:

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

4 ln (c) = ln (c^{4})

= ln ((a + b) (a - b)^{3}) - ln (c^{4})

Apply log rule:

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

ln ((a + b) (a - b)^{3}) - ln (c^{4}) = ln (\frac{( a - b ) ^{3} ( a + b )}{c ^{4}})

= ln (\frac{( a + b ) ( a - b ) ^{3}}{c ^{4}})

- ln (3 x^{2} + 3 x - 10) + ln (2 - 5 x)

ln (a e^{- b t})

2 (ln (5) - ln (2))

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

300 ln (\frac{1000}{2000})

What is ln(a+b)+3ln(a-b)-4ln(c) ?
The solution to ln(a+b)+3ln(a-b)-4ln(c) is ln(((a+b)(a-b)^3)/(c^4))