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Popular >

expand ln((xy)^5)

Solution

expand

ln ((x y)^{5})

Solution

5 ln (x) + 5 ln (y)

Solution steps

ln ((x y)^{5})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x y)^{5}) = 5 ln (x y)

= 5 ln (x y)

Apply log rule:

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

5 ln (x y) = 5 ln (x) + 5 ln (y)

= 5 ln (x) + 5 ln (y)

Popular Examples

expand log_{10}(x/(z^5))expand

lo g_{10} (\frac{x}{z ^{5}})

expand log_{3}((s^2p)^3)expand

lo g_{3} ((s^{2} p)^{3})

simplify log_{10}(x/(1+x))simplify

lo g_{10} (\frac{x}{1 + x})

simplify log_{6}((sqrt(c))/(36))simplify

lo g_{6} (\frac{c}{36})

simplify 72ln(5/6)simplify

72 ln (\frac{5}{6})

Frequently Asked Questions (FAQ)

What is expand ln((xy)^5) ?
The solution to expand ln((xy)^5) is 5ln(x)+5ln(y)