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Popular >

simplify ln(5x^2yz^3)

Solution

simplify

ln (5 x^{2} y z^{3})

Solution

ln (5) + 2 ln (x) + ln (y) + 3 ln (z)

Solution steps

ln (5 x^{2} y z^{3})

Apply log rule:

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

ln (5 x^{2} y z^{3}) = ln (5) + ln (x^{2}) + ln (y) + ln (z^{3})

= ln (5) + ln (x^{2}) + ln (y) + ln (z^{3})

Apply log rule:

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

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

= ln (5) + 2 ln (x) + ln (y) + ln (z^{3})

Apply log rule:

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

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

= ln (5) + 2 ln (x) + ln (y) + 3 ln (z)

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Frequently Asked Questions (FAQ)

What is ln(5x^2yz^3) ?
The solution to ln(5x^2yz^3) is ln(5)+2ln(x)+ln(y)+3ln(z)