Canceling out log2

Question

How would go about cancelling out the $\log_2$. Is it possible for the TI 89 to handle this? I'm not sure how to put $\log_2$ in my TI 89.

$20=30\cdot \log_2(1+x)$

Answer 1

$$\log_b a = \frac{\log_{X} a}{\log_{X} b},$$

where $X$ is whatever you want it to be, usually either $e$ (e.g. $\ln$) or $10$. It doesn't matter! Literally any $X$ will work, so whatever your calculator uses as its default base, just use that and do log(a)/log(b).

Answer 2

$\log_2(x+1)=\frac{20}{30}=\frac{2}{3}\implies x+1=2^{\frac{2}{3}}=(\sqrt[3]{2})^2\implies x=(\sqrt[3]{2})^2-1$