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Popular >

simplify ln(xy^8z^9)

Solution

simplify

ln (x y^{8} z^{9})

Solution

ln (x) + 8 ln (y) + 9 ln (z)

Solution steps

ln (x y^{8} z^{9})

Apply log rule:

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

ln (x y^{8} z^{9}) = ln (x) + ln (y^{8}) + ln (z^{9})

= ln (x) + ln (y^{8}) + ln (z^{9})

Apply log rule:

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

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

= ln (x) + 8 ln (y) + ln (z^{9})

Apply log rule:

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

ln (z^{9}) = 9 ln (z)

= ln (x) + 8 ln (y) + 9 ln (z)

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Frequently Asked Questions (FAQ)

What is ln(xy^8z^9) ?
The solution to ln(xy^8z^9) is ln(x)+8ln(y)+9ln(z)