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Popular >

simplify ln(36*15^{1/2})+c

Solution

simplify

ln (36 \cdot 1 5^{\frac{1}{2}}) + c

Solution

2 ln (6) + \frac{1}{2} ln (15) + c

Solution steps

ln (36 \cdot 1 5^{\frac{1}{2}}) + c

Apply log rule:

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

ln (36 \cdot 1 5^{\frac{1}{2}}) = ln (36) + ln (1 5^{\frac{1}{2}})

= ln (36) + ln (1 5^{\frac{1}{2}}) + c

Apply log rule:

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

ln (1 5^{\frac{1}{2}}) = \frac{1}{2} ln (15)

= ln (36) + \frac{1}{2} ln (15) + c

ln (36) = 2 ln (6)

= 2 ln (6) + \frac{1}{2} ln (15) + c

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Frequently Asked Questions (FAQ)

What is ln(36*15^{1/2})+c ?
The solution to ln(36*15^{1/2})+c is 2ln(6)+1/2 ln(15)+c