What is 5ln(x-6)-ln(x^2-11x+30)+2ln(x-5) ?

The solution to 5ln(x-6)-ln(x^2-11x+30)+2ln(x-5) is ln((x-6)^4(x-5))

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simplify 5ln(x-6)-ln(x^2-11x+30)+2ln(x-5)

simplify

5 ln (x - 6) - ln (x^{2} - 11 x + 30) + 2 ln (x - 5)

ln ((x - 6)^{4} (x - 5))

Solution steps

5 ln (x - 6) - ln (x^{2} - 11 x + 30) + 2 ln (x - 5)

Apply log rule:

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

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

= ln ((x - 6)^{5}) - ln (x^{2} - 11 x + 30) + 2 ln (x - 5)

Apply log rule:

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

ln ((x - 6)^{5}) - ln (x^{2} - 11 x + 30) = ln (\frac{( x - 6 ) ^{5}}{x ^{2} - 11 x + 30})

= ln (\frac{( x - 6 ) ^{5}}{x ^{2} - 11 x + 30}) + 2 ln (x - 5)

Simplify

\frac{( x - 6 ) ^{5}}{x ^{2} - 11 x + 30} : \frac{( x - 6 ) ^{4}}{x - 5}

= ln (\frac{( x - 6 ) ^{4}}{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 - 6 ) ^{4}}{x - 5}) + ln ((x - 5)^{2})

Apply log rule:

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

ln (\frac{( x - 6 ) ^{4}}{x - 5}) + ln ((x - 5)^{2}) = ln (\frac{( x - 6 ) ^{4}}{x - 5} (x - 5)^{2})

= ln (\frac{( x - 6 ) ^{4}}{x - 5} (x - 5)^{2})

Simplify

\frac{( x - 6 ) ^{4}}{x - 5} (x - 5)^{2} : (x - 6)^{4} (x - 5)

= ln ((x - 6)^{4} (x - 5))

5 ln (x + 1) + 6 ln (x)

\frac{1}{2} lo g_{10} (b) + 5 lo g_{10} (c)

ln (\frac{81162081}{390625})

lo g_{10} (\frac{6 x}{x + 2})

ln (\frac{5}{10})

What is 5ln(x-6)-ln(x^2-11x+30)+2ln(x-5) ?
The solution to 5ln(x-6)-ln(x^2-11x+30)+2ln(x-5) is ln((x-6)^4(x-5))