How do I find the base when Log is given

I'm trying to figure out how to calculate the base if:

$$ \log_b 30 = 0.30290 $$

How do I find $b$ ?

I've slaved over the Wikipedia page for logarithms, but I just don't get the mathematical notations.

If someone could let me know the steps to find $b$ in plain english, I'd be eternally grateful!

You need to think about the definitions.

Since $a^b=c$ can be rewritten as $\log_a c = b$.

That should tell you that,

$$b^{0.30290} = 30$$

and then,

$$b = \exp {\frac{\ln 30}{0.30290}} $$

The change-of-base identity says the following: fixing $\ln$ to mean the natural logarithm (logarithm with base $e$), $$ \log_b x = \frac{\ln x}{\ln b} $$ and as a consequence, you can derive the statement that $$ \log_b x = \frac{1}{\log_x b}. $$

This tells you that your statement $$ \log_b 30 = 0.30290 $$ is equivalent to $$ \log_{30} b = \frac{1}{0.30290}$$ so that

$$ b = 30^{\frac{1}{0.30290}} \sim 75265.70 $$