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

Jul 16, 2016

${\log}_{b} \left(4 {b}^{2}\right) = 2 a + 2$

#### Explanation:

As ${\log}_{b} 2 = a$ and ${\log}_{b} 3 = c$, we have ${b}^{a} = 2$ and ${b}^{c} = 3$

Let ${\log}_{b} \left(4 {b}^{2}\right) = x$, then

b^x=4b^2=2^2×b^2

= (b^a)^2×b^2

= ${b}^{2 a + 2}$

Hence $x = 2 a + 2$ i.e. ${\log}_{b} \left(4 {b}^{2}\right) = 2 a + 2$