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Popular >

simplify ln(AB^n)

Solution

simplify

ln (A B^{n})

Solution

ln (A) + n ln (B)

Solution steps

ln (A B^{n})

Apply log rule:

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

ln (A B^{n}) = ln (A) + ln (B^{n})

= ln (A) + ln (B^{n})

Apply log rule:

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

ln (B^{n}) = n ln (B)

= ln (A) + n ln (B)

Popular Examples

simplify ln(8x^3y^5)simplify

ln (8 x^{3} y^{5})

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lo g_{8} (\frac{1 2 ^{6}}{7 ^{2}})

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ln (5) + 2 ln (x) + 3 (x^{2} + 5)

simplify (28)/(0.693)*ln(100/9)simplify

\frac{28}{0.693} \cdot ln (\frac{100}{9})

Frequently Asked Questions (FAQ)

What is ln(AB^n) ?
The solution to ln(AB^n) is ln(A)+nln(B)