# Thread: Solving Exponential Equations Using Logs

1. ## Solving Exponential Equations Using Logs

Hello everyone.

I was honing my skills at a variety of previous learned math operations and found one that I was unable to solve.

125n^(x)=n^(x+3), n can not equal zero then 125n is equal to?

From checking and guessing I was able to get n=5 then confirmed that with a graphing utility. Unfortunately, I always get stuck solving 125n^(x)=n^(x+3) algebraically using logs. Could someone walk me through the steps involved to isolate the variable n

Thanks a lot.

2. Divide both sides by $n^x$!

$\frac{125n^x}{n^x}= \frac{n^{x+3}}{n^x}$
$125= 5^3= n^3$ which tells us that n= 5.

With n= 5, your equation is true for all x. With n any number other than 5, it is false for all x.