What is 4ln(x-5)-ln(x^2-8x+15)+2ln(x-3) ?

The solution to 4ln(x-5)-ln(x^2-8x+15)+2ln(x-3) is ln((x-5)^3(x-3))

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simplify 4ln(x-5)-ln(x^2-8x+15)+2ln(x-3)

simplify

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

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

Solution steps

4 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})

4 ln (x - 5) = ln ((x - 5)^{4})

= ln ((x - 5)^{4}) - 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)^{4}) - ln (x^{2} - 8 x + 15) = ln (\frac{( x - 5 ) ^{4}}{x ^{2} - 8 x + 15})

= ln (\frac{( x - 5 ) ^{4}}{x ^{2} - 8 x + 15}) + 2 ln (x - 3)

Simplify

\frac{( x - 5 ) ^{4}}{x ^{2} - 8 x + 15} : \frac{( x - 5 ) ^{3}}{x - 3}

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

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

Simplify

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

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

25 lo g_{5} (x) + 5 lo g_{5} (y)

ln (\frac{x ^{5} x + 2}{x + 8})

\frac{1}{5} ln (\frac{x - 1}{x ^{2} - x + 1})

lo g_{10} (\frac{2 x ( 1 - 5 x ) ^{\frac{3}{2}}}{( x + 4 ) ^{3}})

ln (\frac{0.075}{0.06})

What is 4ln(x-5)-ln(x^2-8x+15)+2ln(x-3) ?
The solution to 4ln(x-5)-ln(x^2-8x+15)+2ln(x-3) is ln((x-5)^3(x-3))