Sorry for this type of question, but I've forgotten the math basic from middle school, maybe someone can help me out. If I know the result and base, how can I calculate exponent?
$2.5 = 10^x$, how would I get the $x$ value of this?
[Math] How to get exponent of power if base is known
exponentiation
Best Answer
Do you remember the definition of logarithm? That's exactly what you need because the logarithm is defined as the inverse operation of exponentiation (raising a number to a power):
$$ 2.5=10^x \Longleftrightarrow x=\log_{10}{2.5}. $$
The statement $x=\log_{b}{a}$ is asking the question what power should I raise $b$ to get $a$? And that's equivalent to saying $b^x=a$.