What is ln((x^2-7)/((x-3)^4)) ?

The solution to ln((x^2-7)/((x-3)^4)) is ln(x^2-7)-4ln(x-3)

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simplify ln((x^2-7)/((x-3)^4))

simplify

ln (\frac{x ^{2} - 7}{( x - 3 ) ^{4}})

ln (x^{2} - 7) - 4 ln (x - 3)

Solution steps

ln (\frac{x ^{2} - 7}{( x - 3 ) ^{4}})

Apply log rule:

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

ln (\frac{x ^{2} - 7}{( x - 3 ) ^{4}}) = ln (x^{2} - 7) - ln ((x - 3)^{4})

= ln (x^{2} - 7) - ln ((x - 3)^{4})

Apply log rule:

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

ln ((x - 3)^{4}) = 4 ln (x - 3)

= ln (x^{2} - 7) - 4 ln (x - 3)

ln (2 x - 1) - ln (x + 4)

lo g_{10} (4^{- 1}) + lo g_{10} (\frac{1}{2})

lo g_{10} (\frac{3 a ^{3}}{5 b})

ln (a e^{- a x})

\frac{1}{5} lo g_{b} (x^{6} y^{7}) - \frac{5}{7} lo g_{b} (x^{3} y)

What is ln((x^2-7)/((x-3)^4)) ?
The solution to ln((x^2-7)/((x-3)^4)) is ln(x^2-7)-4ln(x-3)