What is 5ln(x-4)-ln(x^2-9x+20)+2ln(x-5) ?

The solution to 5ln(x-4)-ln(x^2-9x+20)+2ln(x-5) is ln((x-4)^4(x-5))

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simplify 5ln(x-4)-ln(x^2-9x+20)+2ln(x-5)

simplify

5 ln (x - 4) - ln (x^{2} - 9 x + 20) + 2 ln (x - 5)

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

Solution steps

5 ln (x - 4) - ln (x^{2} - 9 x + 20) + 2 ln (x - 5)

Apply log rule:

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

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

= ln ((x - 4)^{5}) - ln (x^{2} - 9 x + 20) + 2 ln (x - 5)

Apply log rule:

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

ln ((x - 4)^{5}) - ln (x^{2} - 9 x + 20) = ln (\frac{( x - 4 ) ^{5}}{x ^{2} - 9 x + 20})

= ln (\frac{( x - 4 ) ^{5}}{x ^{2} - 9 x + 20}) + 2 ln (x - 5)

Simplify

\frac{( x - 4 ) ^{5}}{x ^{2} - 9 x + 20} : \frac{( x - 4 ) ^{4}}{x - 5}

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

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

Simplify

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

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

lo g_{2} (a c) - \frac{1}{4} lo g_{8} (b)

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

lo g_{10} (x^{e} e^{x})

2 + lo g_{10} (\frac{8}{0.1})

0.935 \cdot ln (\frac{39 + 273}{337 + 273})

What is 5ln(x-4)-ln(x^2-9x+20)+2ln(x-5) ?
The solution to 5ln(x-4)-ln(x^2-9x+20)+2ln(x-5) is ln((x-4)^4(x-5))