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! 
 A: Once you have log of one base (e.g. the natural log $\ln$), you can easily calculate the log of any basis via
$$\log_b a = \frac{\ln a}{\ln b}.$$
In your case you want to solve $\log_b a =c$ for $b$, which is easily done using the formula above with the solution
$$ \ln b = \frac{\ln a}{c}$$
or equivalently
$$b = \exp \left( \frac{\ln a}{c} \right).$$
A: 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, 
$$b = \exp {\frac{\ln 30}{0.30290}} $$
A: 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 
$$ b = 30^{\frac{1}{0.30290}} \sim 75265.70 $$
A: In Excel: to quickly calculate the elusive "e":
To calculate "e" (the base of LN):
e = x^(1/LN(x))
Wherein: x = any number >or< 1 but > 0
