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Popular >

expand ln(x^2(y-2)^3)

Solution

expand

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

Solution

2 ln (x) + 3 ln (y - 2)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln ((y - 2)^{3}) = 3 ln (y - 2)

= 2 ln (x) + 3 ln (y - 2)

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Frequently Asked Questions (FAQ)

What is expand ln(x^2(y-2)^3) ?
The solution to expand ln(x^2(y-2)^3) is 2ln(x)+3ln(y-2)