Use properties of logarithms to expand each logarithmic expr

Use properties of logarithms to expand each logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. log_b (y^4 z)

Solution

log_b(y^4z)

Use the following log properties to solve :

log(a^x) = a*logx ; log(a*b) = loga +logb ; log_ab = log(b) / log(a)

log_b(y^4z) = 4zlog_b(y)

= 4z{ log(y) / log(b) }