What is 6ln(x-3)-ln(x^2-8x+15)+2ln(x-5) ?

The solution to 6ln(x-3)-ln(x^2-8x+15)+2ln(x-5) is ln((x-3)^5(x-5))

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simplify 6ln(x-3)-ln(x^2-8x+15)+2ln(x-5)

simplify

6 ln (x - 3) - ln (x^{2} - 8 x + 15) + 2 ln (x - 5)

ln ((x - 3)^{5} (x - 5))

Solution steps

6 ln (x - 3) - ln (x^{2} - 8 x + 15) + 2 ln (x - 5)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

6 ln (x - 3) = ln ((x - 3)^{6})

= ln ((x - 3)^{6}) - ln (x^{2} - 8 x + 15) + 2 ln (x - 5)

Apply log rule:

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

ln ((x - 3)^{6}) - ln (x^{2} - 8 x + 15) = ln (\frac{( x - 3 ) ^{6}}{x ^{2} - 8 x + 15})

= ln (\frac{( x - 3 ) ^{6}}{x ^{2} - 8 x + 15}) + 2 ln (x - 5)

Simplify

\frac{( x - 3 ) ^{6}}{x ^{2} - 8 x + 15} : \frac{( x - 3 ) ^{5}}{x - 5}

= ln (\frac{( x - 3 ) ^{5}}{x - 5}) + 2 ln (x - 5)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (x - 5) = ln ((x - 5)^{2})

= ln (\frac{( x - 3 ) ^{5}}{x - 5}) + ln ((x - 5)^{2})

Apply log rule:

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

ln (\frac{( x - 3 ) ^{5}}{x - 5}) + ln ((x - 5)^{2}) = ln (\frac{( x - 3 ) ^{5}}{x - 5} (x - 5)^{2})

= ln (\frac{( x - 3 ) ^{5}}{x - 5} (x - 5)^{2})

Simplify

\frac{( x - 3 ) ^{5}}{x - 5} (x - 5)^{2} : (x - 3)^{5} (x - 5)

= ln ((x - 3)^{5} (x - 5))

ln (a e^{(- k t)})

ln (6) + ln (\frac{e ^{(2.47909)}}{3})

- lo g_{10} (9.3 \cdot 1 0^{- 11})

ln (\frac{27}{12})

ln (a^{2} \cdot e) - ln (\frac{1}{a}) - ln (e^{2})

What is 6ln(x-3)-ln(x^2-8x+15)+2ln(x-5) ?
The solution to 6ln(x-3)-ln(x^2-8x+15)+2ln(x-5) is ln((x-3)^5(x-5))