What is 5ln(x-6)-ln(x^2-10x+24)+2ln(x-4) ?

The solution to 5ln(x-6)-ln(x^2-10x+24)+2ln(x-4) is ln((x-6)^4(x-4))

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simplify 5ln(x-6)-ln(x^2-10x+24)+2ln(x-4)

simplify

5 ln (x - 6) - ln (x^{2} - 10 x + 24) + 2 ln (x - 4)

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

Solution steps

5 ln (x - 6) - ln (x^{2} - 10 x + 24) + 2 ln (x - 4)

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} - 10 x + 24) + 2 ln (x - 4)

Apply log rule:

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

ln ((x - 6)^{5}) - ln (x^{2} - 10 x + 24) = ln (\frac{( x - 6 ) ^{5}}{x ^{2} - 10 x + 24})

= ln (\frac{( x - 6 ) ^{5}}{x ^{2} - 10 x + 24}) + 2 ln (x - 4)

Simplify

\frac{( x - 6 ) ^{5}}{x ^{2} - 10 x + 24} : \frac{( x - 6 ) ^{4}}{x - 4}

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

ln (\frac{( \frac{17}{3} )}{19})

2 lo g_{3} (x) + lo g_{3} (a)

\frac{1}{6} ((ln ∣ 1 - 3 ∣ - ln ∣ 0 - 3 ∣) - (ln ∣ 1 + 3 ∣ - ln ∣ 0 + 3 ∣))

- lo g_{10} (6.38 \cdot 1 0^{- 6})

\frac{1}{6} [5 ln (x + 9) - ln (x) - ln (x^{2} - 4)]

What is 5ln(x-6)-ln(x^2-10x+24)+2ln(x-4) ?
The solution to 5ln(x-6)-ln(x^2-10x+24)+2ln(x-4) is ln((x-6)^4(x-4))