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Popular >

expand ln((x^5y)^5)

Solution

expand

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

Solution

25 ln (x) + 5 ln (y)

Solution steps

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

Apply log rule:

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

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

= 5 ln (x^{5} y)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply the numbers:

5 \cdot 5 = 25

= 25 ln (x) + 5 ln (y)

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Frequently Asked Questions (FAQ)

What is expand ln((x^5y)^5) ?
The solution to expand ln((x^5y)^5) is 25ln(x)+5ln(y)