What is simplify-5/2 ln|u+5|+5/2 ln|u-5| ?

The solution to simplify-5/2 ln|u+5|+5/2 ln|u-5| is ln(sqrt((|u-5|^5)/(|u+5|^5)))

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simplify-5/2 ln|u+5|+5/2 ln|u-5|

simplify

- \frac{5}{2} ln ∣ u + 5 ∣ + \frac{5}{2} ln ∣ u - 5 ∣

ln (\frac{∣ u - 5 ∣ ^{5}}{∣ u + 5 ∣ ^{5}})

Solution steps

- \frac{5}{2} ln ∣ u + 5 ∣ + \frac{5}{2} ln ∣ u - 5 ∣

Apply log rule:

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

\frac{5}{2} ln ∣ u + 5 ∣ = ln (∣ u + 5 ∣^{\frac{5}{2}})

= - ln (∣ u + 5 ∣^{\frac{5}{2}}) + \frac{5}{2} ln ∣ u - 5 ∣

Apply log rule:

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

\frac{5}{2} ln ∣ u - 5 ∣ = ln (∣ u - 5 ∣^{\frac{5}{2}})

= - ln (∣ u + 5 ∣^{\frac{5}{2}}) + ln (∣ u - 5 ∣^{\frac{5}{2}})

Apply log rule:

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

ln (∣ u - 5 ∣^{\frac{5}{2}}) - ln (∣ u + 5 ∣^{\frac{5}{2}}) = ln (\frac{∣ u - 5 ∣ ^{\frac{5}{2}}}{∣ u + 5 ∣ ^{\frac{5}{2}}})

= ln (\frac{∣ u - 5 ∣ ^{\frac{5}{2}}}{∣ u + 5 ∣ ^{\frac{5}{2}}})

Combine same powers :

= ln (\frac{∣ u - 5 ∣ ^{5}}{∣ u + 5 ∣ ^{5}})

lo g_{b} (u^{9} v^{8})

ln (5 e^{5 x})

lo g_{a} (y^{3}) - 3 lo g_{a} (y)

lo g_{2} (32 a^{3})

lo g_{3} (7 x^{2})

What is simplify-5/2 ln|u+5|+5/2 ln|u-5| ?
The solution to simplify-5/2 ln|u+5|+5/2 ln|u-5| is ln(sqrt((|u-5|^5)/(|u+5|^5)))