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Popular >

simplify ln(x^8y^3z)

Solution

simplify

ln (x^{8} y^{3} z)

Solution

8 ln (x) + 3 ln (y) + ln (z)

Solution steps

ln (x^{8} y^{3} z)

Apply log rule:

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

ln (x^{8} y^{3} z) = ln (x^{8}) + ln (y^{3}) + ln (z)

= ln (x^{8}) + ln (y^{3}) + ln (z)

Apply log rule:

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

ln (x^{8}) = 8 ln (x)

= 8 ln (x) + ln (y^{3}) + ln (z)

Apply log rule:

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

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

= 8 ln (x) + 3 ln (y) + ln (z)

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Frequently Asked Questions (FAQ)

What is ln(x^8y^3z) ?
The solution to ln(x^8y^3z) is 8ln(x)+3ln(y)+ln(z)