What is ln(x^2-13x+36)+2ln(x-4)-ln(x-9) ?

The solution to ln(x^2-13x+36)+2ln(x-4)-ln(x-9) is ln((x-4)^3)

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simplify ln(x^2-13x+36)+2ln(x-4)-ln(x-9)

simplify

ln (x^{2} - 13 x + 36) + 2 ln (x - 4) - ln (x - 9)

ln ((x - 4)^{3})

Solution steps

ln (x^{2} - 13 x + 36) + 2 ln (x - 4) - ln (x - 9)

Apply log rule:

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

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

= ln (x^{2} - 13 x + 36) + ln ((x - 4)^{2}) - ln (x - 9)

Apply log rule:

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

ln (x^{2} - 13 x + 36) + ln ((x - 4)^{2}) = ln ((x - 4)^{2} (x^{2} - 13 x + 36))

= ln ((x^{2} - 13 x + 36) (x - 4)^{2}) - ln (x - 9)

Apply log rule:

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

ln ((x^{2} - 13 x + 36) (x - 4)^{2}) - ln (x - 9) = ln (\frac{( x - 4 ) ^{2} ( x ^{2} - 13 x + 36 )}{x - 9})

= ln (\frac{( x ^{2} - 13 x + 36 ) ( x - 4 ) ^{2}}{x - 9})

Simplify

\frac{( x ^{2} - 13 x + 36 ) ( x - 4 ) ^{2}}{x - 9} : (x - 4)^{3}

= ln ((x - 4)^{3})

lo g_{6} (\frac{216}{y})

4 lo g_{10} (x y) - 3 lo g_{10} (yz)

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

lo g_{10} (\frac{x}{1000000})

lo g_{10} (2 x) - lo g_{10} (8 x^{3})

What is ln(x^2-13x+36)+2ln(x-4)-ln(x-9) ?
The solution to ln(x^2-13x+36)+2ln(x-4)-ln(x-9) is ln((x-4)^3)