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Popular >

expand ln(y^3(x-2)^4)

Solution

expand

ln (y^{3} (x - 2)^{4})

Solution

3 ln (y) + 4 ln (x - 2)

Solution steps

ln (y^{3} (x - 2)^{4})

Apply log rule:

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

ln (y^{3} (x - 2)^{4}) = ln (y^{3}) + ln ((x - 2)^{4})

= ln (y^{3}) + ln ((x - 2)^{4})

Apply log rule:

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

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

= 3 ln (y) + ln ((x - 2)^{4})

Apply log rule:

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

ln ((x - 2)^{4}) = 4 ln (x - 2)

= 3 ln (y) + 4 ln (x - 2)

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Frequently Asked Questions (FAQ)

What is expand ln(y^3(x-2)^4) ?
The solution to expand ln(y^3(x-2)^4) is 3ln(y)+4ln(x-2)