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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

6 ln (x - 5) = ln ((x - 5)^{6})

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

Apply log rule:

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

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

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

Simplify

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

2 ln (x - 3) - ln (6) - 3 ln (x + 2)

\frac{1}{2} ln ∣ x - 2 ∣ + \frac{1}{2} ln ∣ x + 2 ∣

ln (\frac{x ^{2} y}{4 e ^{5} y ^{3}})

ln (x^{2}) + 2 ln (x) + 1

\frac{1}{0.04} ln (\frac{72}{72 - 42})

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