simplify ln(ab^x)

Solution

simplify

ln (a b^{x})

ln (a) + x ln (b)

Solution steps

ln (a b^{x})

Apply log rule:

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

ln (a b^{x}) = ln (a) + ln (b^{x})

= ln (a) + ln (b^{x})

Apply log rule:

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

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

= ln (a) + x ln (b)

ln (x^{2} - 1) - 2 ln (x + 1) + ln (x^{2} + x)

lo g_{10} (x^{3} z)

2 ln (x) + 3 ln (y) - 4 ln (z)

\frac{9 ln ( 5 )}{2 ln ( 3 ) - ln ( 5 )}

lo g_{10} (3 x + 10) - lo g_{10} (x)