What is ln((a^{-2})/(b^4c^{-3)}) ?

The solution to ln((a^{-2})/(b^4c^{-3)}) is -2ln(a)-4ln(b)+3ln(c)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((a^{-2})/(b^4c^{-3)})

simplify

ln (\frac{a ^{- 2}}{b ^{4} c ^{- 3}})

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

Solution steps

ln (\frac{a ^{- 2}}{b ^{4} c ^{- 3}})

Apply log rule:

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

ln (\frac{a ^{- 2}}{b ^{4} c ^{- 3}}) = ln (a^{- 2}) - ln (b^{4} c^{- 3})

= ln (a^{- 2}) - ln (b^{4} c^{- 3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (a^{- 2}) = - 2 ln (a)

= - 2 ln (a) - ln (b^{4} c^{- 3})

Apply log rule:

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

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

= - 2 ln (a) - (ln (b^{4}) + ln (c^{- 3}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= - 2 ln (a) - (4 ln (b) + ln (c^{- 3}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (c^{- 3}) = - 3 ln (c)

= - 2 ln (a) - (4 ln (b) - 3 ln (c))

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

= - 2 ln (a) - 4 ln (b) + 3 ln (c)

ln (\frac{y}{2} \cdot e^{- y ∣ x ∣})

ln 1 + e^{8 I n} - ln (3)

ln (\frac{0.015}{0.025})

lo g_{8} (z x \cdot y)

\frac{1}{3} (ln (11) - ln (4))

What is ln((a^{-2})/(b^4c^{-3)}) ?
The solution to ln((a^{-2})/(b^4c^{-3)}) is -2ln(a)-4ln(b)+3ln(c)