simplify ln(3^ba^b)

Solution

simplify

ln (3^{b} a^{b})

b ln (3) + b ln (a)

Solution steps

ln (3^{b} a^{b})

Apply log rule:

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

ln (3^{b} a^{b}) = ln (3^{b}) + ln (a^{b})

= ln (3^{b}) + ln (a^{b})

Apply log rule:

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

ln (3^{b}) = b ln (3)

= b ln (3) + ln (a^{b})

Apply log rule:

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

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

= b ln (3) + b ln (a)

2 lo g_{4} (y - 1) - lo g_{4} (y + 3) - 1

lo g_{10} (a^{6} b^{4})

3 ln (2) + 2 ln (x) - 12 ln (x + 4)

3 lo g_{2} (x) + lo g_{2} (y) - 5 lo g_{2} (z)

lo g_{5} (1000) + lo g_{4 a} (64 a^{3})