Question

Suppose `Log_b2=a` and `Log_b3=c`, how do you find `Log_b(4b^2)`?

Answer 1

`log_b(4b^2)=2a+2`

Explanation:

As `log_b2=a` and `log_b3=c`, we have `b^a=2` and `b^c=3`

Let `log_b(4b^2)=x`, then

`b^x=4b^2=2^2×b^2`

= `(b^a)^2×b^2`

= `b^(2a+2)`

Hence `x=2a+2` i.e. `log_b(4b^2)=2a+2`