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Popular >

simplify ln(zx^2*y^5)

Solution

simplify

ln (z x^{2} \cdot y^{5})

Solution

ln (z) + 2 ln (x) + 5 ln (y)

Solution steps

ln (z x^{2} y^{5})

Apply log rule:

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

ln (z x^{2} y^{5}) = ln (z) + ln (x^{2}) + ln (y^{5})

= ln (z) + ln (x^{2}) + ln (y^{5})

Apply log rule:

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

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

= ln (z) + 2 ln (x) + ln (y^{5})

Apply log rule:

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

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

= ln (z) + 2 ln (x) + 5 ln (y)

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Frequently Asked Questions (FAQ)

What is ln(zx^2*y^5) ?
The solution to ln(zx^2*y^5) is ln(z)+2ln(x)+5ln(y)