How do I find an unknown power in this formula? $$    \frac{1}{2^a} = 3.0988$$
How do I solve for $a$?
The original equation was:
$$\frac{1}{i^a}-\left(B-\frac{NE}{P_1-E}\right) = 0$$
I know that: 


*

*$B=10000$

*$N = 50$

*$E = 15$

*$P_1 = 3000$


$$\frac1{i^a}-\left(10000-\frac{50(15)}{3000-15}\right) = 0$$
$$\frac1{i^a} - 3.0988 = 0$$
so if $i = 2$ how do I solve for $a$?

Using $\frac{1}{2^a} = 3.0988$,
$$\begin{align}
\ln\left(\frac {1}{2^a}\right) &= \ln\left(3.0988\right) \\ 
\ln\left(1\right) - \ln\left(2^a\right) &= \ln\left(3.0988\right) \\
0 - \ln\left(2^a\right) &= \ln\left(3.0988\right) \\
\ln\left(2^a\right) &= - \ln\left(3.0988\right) \\
a\ln\left(2\right) &= -\ln\left(3.0988\right) \\
a &= \frac{- \ln\left(3.0988\right)} {\ln\left(2\right)}
\end{align}$$
Or you simply work in $\log_2$:
$$\begin{align}
\frac{1}{2^a} &= 3.0988 \\
2^0 &= 2^a 2^{\log_2 3.0988 } \\
0 &= a+ \log_2 3.0988 \\
a&=-\log_2 3.0988
\end{align}$$
