# How do you find the power of $x$? [closed]

For example with $5^x=125$. How do you manipulate the equation to find $x$?

• In this case you are probably expected to recognize that $5^3=125$. Mar 9, 2015 at 5:25

we have: $$5^x = 125$$ $$\log(5^x) = \log(125)$$ $$x\log(5) = \log(125)$$ $$x = \frac{\log(125)}{\log(5)}$$ Can you guess the answer ?

• oh yeah, thank you. just fixed it Mar 9, 2015 at 5:30
• Knew the answer, just used a simple example Mar 9, 2015 at 7:34

By taking logarithm for both sides, we should have: $$\log (5^x) = \log(125)$$

one of the main properties of logarithm functions is that you can take the power out of the logarithm, so we would have:

$$x \log(5) = \log(125)$$

solve for $x$ and you're done..

Here is one possible solution: \begin{aligned}5^x&=125\\ {5^x}/5&={125}/5\\ 5^{x-1}&=25\\ {5^{x-1}}/5&=5\\ 5^{x-2}&=5\\ \end{aligned} We can conclude that $x-2=1 \implies x=3$.

• One is one of those so-called special cases. :) Mar 9, 2015 at 5:46
• 125/5 = 25 @Jasha Mar 9, 2015 at 5:57
• I've suggested an edit.. @Jasha Mar 9, 2015 at 5:59