What is ln(1/a (x-3)^{-3}) ?

The solution to ln(1/a (x-3)^{-3}) is -3ln(x-3)-ln(a)

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simplify ln(1/a (x-3)^{-3})

simplify

ln (\frac{1}{a} (x - 3)^{- 3})

- 3 ln (x - 3) - ln (a)

Solution steps

ln (\frac{1}{a} (x - 3)^{- 3})

Apply log rule:

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

ln (\frac{1}{a} (x - 3)^{- 3}) = ln (\frac{1}{a}) + ln ((x - 3)^{- 3})

= ln (\frac{1}{a}) + ln ((x - 3)^{- 3})

Apply log rule:

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

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

= ln (\frac{1}{a}) - 3 ln (x - 3)

Apply log rule:

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

ln (\frac{1}{a}) = ln (1) - ln (a)

= ln (1) - ln (a) - 3 ln (x - 3)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (a) - 3 ln (x - 3)

0 - ln (a) - 3 ln (x - 3) = - ln (a) - 3 ln (x - 3)

= - 3 ln (x - 3) - ln (a)

ln (y) + ln (2 x)

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ln (\frac{s ^{2} + 1}{( s + 2 ) ^{2}})

lo g_{6} (5) + 2 lo g_{6} (x + 1)

\frac{1}{5} (2 ln (2) - ln (3))

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