What is ln((a^{-1})/(b^2c^3)) ?

The solution to ln((a^{-1})/(b^2c^3)) is -ln(a)-2ln(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^{-1})/(b^2c^3))

simplify

ln (\frac{a ^{- 1}}{b ^{2} c ^{3}})

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

Solution steps

ln (\frac{a ^{- 1}}{b ^{2} c ^{3}})

Apply log rule:

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

ln (\frac{a ^{- 1}}{b ^{2} c ^{3}}) = ln (a^{- 1}) - ln (b^{2} c^{3})

= ln (a^{- 1}) - ln (b^{2} c^{3})

Apply log rule:

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

ln (a^{- 1}) = - 1 \cdot ln (a)

= - 1 \cdot ln (a) - ln (b^{2} c^{3})

Apply log rule:

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

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

= - 1 \cdot ln (a) - (ln (b^{2}) + ln (c^{3}))

Apply log rule:

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

ln (b^{2}) = 2 ln (b)

= - 1 \cdot ln (a) - (2 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)

= - 1 \cdot ln (a) - (2 ln (b) + 3 ln (c))

Multiply:

1 \cdot ln (a) = ln (a)

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

- (2 ln (b) + 3 ln (c)) : - 2 ln (b) - 3 ln (c)

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

- 4 lo g_{10} (0.03 x)

- lo g_{10} (1.24 \cdot 1 0^{4})

ln (x) + ln (y) - 2 x - 2 y + 2

4.76 + lo g_{10} (\frac{0.5}{3})

ln (\frac{302.12}{398})

What is ln((a^{-1})/(b^2c^3)) ?
The solution to ln((a^{-1})/(b^2c^3)) is -ln(a)-2ln(b)-3ln(c)