What is 13ln(x)-12ln(x^2+16) ?

The solution to 13ln(x)-12ln(x^2+16) is ln((x^{13})/((x^2+16)^{12)})

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simplify 13ln(x)-12ln(x^2+16)

simplify

13 ln (x) - 12 ln (x^{2} + 16)

ln (\frac{x ^{13}}{( x ^{2} + 16 ) ^{12}})

Solution steps

13 ln (x) - 12 ln (x^{2} + 16)

Apply log rule:

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

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

= ln (x^{13}) - 12 ln (x^{2} + 16)

Apply log rule:

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

12 ln (x^{2} + 16) = ln ((x^{2} + 16)^{12})

= ln (x^{13}) - ln ((x^{2} + 16)^{12})

Apply log rule:

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

ln (x^{13}) - ln ((x^{2} + 16)^{12}) = ln (\frac{x ^{13}}{( x ^{2} + 16 ) ^{12}})

= ln (\frac{x ^{13}}{( x ^{2} + 16 ) ^{12}})

lo g_{3} (u^{2}) - lo g_{3} (v)

lo g_{2} ((\frac{b}{c})^{4})

lo g_{t} (X \cdot Y)

ln (x^{4}) - ln (x^{16})

7 lo g_{2} (x) + 4 lo g_{2} (y) - 3 lo g_{2} (z)

What is 13ln(x)-12ln(x^2+16) ?
The solution to 13ln(x)-12ln(x^2+16) is ln((x^{13})/((x^2+16)^{12)})