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Popular >

simplify ln(x^3y^4z^5)

Solution

simplify

ln (x^{3} y^{4} z^{5})

Solution

3 ln (x) + 4 ln (y) + 5 ln (z)

Solution steps

ln (x^{3} y^{4} z^{5})

Apply log rule:

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

ln (x^{3} y^{4} z^{5}) = ln (x^{3}) + ln (y^{4}) + ln (z^{5})

= ln (x^{3}) + ln (y^{4}) + ln (z^{5})

Apply log rule:

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

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

= 3 ln (x) + ln (y^{4}) + ln (z^{5})

Apply log rule:

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

ln (y^{4}) = 4 ln (y)

= 3 ln (x) + 4 ln (y) + ln (z^{5})

Apply log rule:

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

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

= 3 ln (x) + 4 ln (y) + 5 ln (z)

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Frequently Asked Questions (FAQ)

What is ln(x^3y^4z^5) ?
The solution to ln(x^3y^4z^5) is 3ln(x)+4ln(y)+5ln(z)