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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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^{- 3} c^{2})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

ln (\frac{10000}{8600})

ln (x^{3}) + ln (y)

ln (\frac{1 + 8}{2 + 16})

- \frac{2 ln ( 10 ) + ln ( 97 )}{6}

- ln (2.05 e^{- 4})

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