How do you find the exponent with a base that is 7 and the answered equation is 1?

Answer 1

Well first of all, you should know that anything raised to the 0th power is 1. So the answer is 0: 7^0=1.

But if the answer's not so obvious, you should use logarithms. If 7^x=1, then the log (7) of x = 1. So you'd just find the inverse log (base 7) of 1.

Some calculators can do that, some can't. The ones that can't usually can only find the log of a number in base 10 or base e (which is ~2.7182818), so you'd have to do a logarithmic conversion.

To do a logarithmic conversion, you'd have to use the base conversion formula: log (base 7) of x = log (base 10) of x/log (base 10) of 7. Both sides of that equation equals 1 because of the information that you're giving me.

So...

log (base 10) of x/log (base 10) of 7 = 1.

Using algebra, we're going to try to get x by itself on one side of the equation. We'll start by getting rid of the denominator by multiplying both sides by log (base 10) 7. The result:

log (base 10) of x = 1

We'll isolate x from the logarithm by taking the inverse log of the left side. We'll take the inverse log of the right side to maintain the equality.

x = log inverse (base 10) of 1.

You can use a calculator for that. Well, you COULD, but you should have remembered that the log inverse of 1 with base ANYTHING is 0, right?

x = 0.

When you're trying to visualize what's going on, always remember that logarithms are exponents. If 10^2=100, then "2" in that previous equation is a logarithm; it's the base 10 logarithm of 100; log (base 10) of 100 = 2. It's basically a way of switching around the order that each number comes in. That may help you keep this new mathematical language in perspective.