simplify ln(A^xB^y)

Solution

simplify

ln (A^{x} B^{y})

x ln (A) + y ln (B)

Solution steps

ln (A^{x} B^{y})

Apply log rule:

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

ln (A^{x} B^{y}) = ln (A^{x}) + ln (B^{y})

= ln (A^{x}) + ln (B^{y})

Apply log rule:

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

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

= x ln (A) + ln (B^{y})

Apply log rule:

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

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

= x ln (A) + y ln (B)

ln (x^{y} \cdot (1 - x)^{z - y})

0.0259 \cdot ln (\frac{4.7 \cdot 1 0 ^{17}}{1.15 \cdot 1 0 ^{14}})

ln (40) - ln (4)

ln (\frac{y ^{2} + x ^{2}}{x ^{2}})