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Popular >

simplify ln(x^2y^5z)

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Popular Examples

simplify ln(20)-ln(5)simplify

ln (20) - ln (5)

simplify 4log_{10}(2)+4log_{10}(x)simplify

4 lo g_{10} (2) + 4 lo g_{10} (x)

simplify log_{10}(x^3y^5)simplify

lo g_{10} (x^{3} y^{5})

simplify 1/2 (-1/3 ln|y|+1/3 ln|y-3|)simplify

\frac{1}{2} (- \frac{1}{3} ln ∣ y ∣ + \frac{1}{3} ln ∣ y - 3 ∣)

simplify log_{10}(10x)+log_{10}(20y)-log_{10}(10)simplify

lo g_{10} (10 x) + lo g_{10} (20 y) - lo g_{10} (10)

Frequently Asked Questions (FAQ)

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