Answer:
[tex]A=\frac{1}{k}\log_4(\frac{CN}{(N-1)(0.088)})[/tex]
Step-by-step explanation:
Given formula,
[tex]C=(0.088)(4)^{kA} \frac{(N-1)}{N}----(1)[/tex]
For finding the formula for A we need to isolate A in the left side,
From equation (1),
[tex]C=\frac{(0.088)(N-1)}{N}4^{kA}[/tex]
[tex]\frac{CN}{(0.088)(N-1)}=4^{kA}[/tex]
Taking log both sides,
[tex]\log(\frac{CN}{(0.088)(N-1)})=kA \log 4[/tex]
[tex]\implies A=\frac{\log(\frac{CN}{(0.088)(N-1)})}{log 4}[/tex]
[tex]\implies A=\frac{1}{k}\log_4(\frac{CN}{(N-1)(0.088)})[/tex]
[tex](\because \log_bx=\frac{\log_ax}{\log_ab})[/tex]
