What is 13ln(x)-2ln(x^2+12) ?

The solution to 13ln(x)-2ln(x^2+12) is ln((x^{13})/((x^2+12)^2))

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simplify 13ln(x)-2ln(x^2+12)

simplify

13 ln (x) - 2 ln (x^{2} + 12)

ln (\frac{x ^{13}}{( x ^{2} + 12 ) ^{2}})

Solution steps

13 ln (x) - 2 ln (x^{2} + 12)

Apply log rule:

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

13 ln (x) = ln (x^{13})

= ln (x^{13}) - 2 ln (x^{2} + 12)

Apply log rule:

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

2 ln (x^{2} + 12) = ln ((x^{2} + 12)^{2})

= ln (x^{13}) - ln ((x^{2} + 12)^{2})

Apply log rule:

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

ln (x^{13}) - ln ((x^{2} + 12)^{2}) = ln (\frac{x ^{13}}{( x ^{2} + 12 ) ^{2}})

= ln (\frac{x ^{13}}{( x ^{2} + 12 ) ^{2}})

ln ((t x)^{2}) - 2 ln (t y)

e^{3} + ln (16 x)

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

ln (x + 1) + ln (sin (y))

ln (\frac{( 2 x - 1 )}{x - 1})

What is 13ln(x)-2ln(x^2+12) ?
The solution to 13ln(x)-2ln(x^2+12) is ln((x^{13})/((x^2+12)^2))