Question

Solve for x.
3^x-2 = 5

Answer 1

Is the -2 inside the exponent or no? Meaning is the equation (3^x) -2 = 5 or is it 3^(x-2) = 5?

Answer 2

It is.

Answer 3

which one is what he or she is saying

Answer 4

3^(x-2)=5

Answer 5

Okay the first thing you do is separate the 3^x and 3^-2 to get a product. When you do this you should get (3^x)*(3^-2) = 5. Next thing you do is change the 3^-2 to be equal to (1/3^2) which is the same thing as (1/9).

So then your equation should look like (3^x)*(1/9) = 5. Multiply both sides by 9 and you get 3^x = 45. Then do a logarithm to get \[\log_{3} (45) = x\]

Then divide \[\log_{10} (45)/\log_{10} (3) = x \]

You should get a number of something like 3.464973521 on your calculator when you do this. So x = 3.464973521.

To test this plug it back into the original equation 3^(3.464973521-2) = 5 which comes out correct on a calculator.

Answer 6

By the way the base of the first log is 3, it's kind of hard to see so I thought I'd just let you know that.