Question

solve 9^x = 3^(x - 2) for x

Answer 1

@mathmale

Answer 2

I'd be delighted to help you, but need to finish up helping 2 other students first.

Answer 3

Would x = -2 ?

Answer 4

You substitute x=-2 into the original equation abnd see wehther or not that equation is true. if it is, your result, x=-2, is correct.

Answer 5

Okay, I substituted it and x = -2!

Answer 6

2^x = 4^(x + 1)

I think that one would be x = -2 also

Answer 7

Actually, you replace every "x" with the value -2 and then deetermine whether or not the resulting equation is true. Try again, please. Or maybe I misread your response. Unsure.

Answer 8

You got x=-2 already. All I'm asking you to do is to check that by subst. it back into the original equation.

Answer 9

This one is a bit tricky for me



4^x = 10

Answer 10

OK. Remember, I told you I'm completing work with 2 others so please be patient...I promise to be with you as soon as possible.

Answer 11

solve 9^x = 3^(x - 2) for x

What I see here is the following:
x x-2
9 = 3

Hope that's reasonably clear for you.

We're supposed to find the value of x, right?

Answer 12

Well, I have found that one. X = -2


but this one is the one that I am stumped on

4^x = 10

Answer 13

It'd be so much easier if these 2 different bases, 9 and 3, could be modified so that both are powers of the same base.

Note that 2^2 = 4.

Thus, 4 = 2^2.

Basic examples, but perhaps these will help you to understand what I'm aiming at.

take that 9 and rewrite it as 3^2.
Substitute (3^2) for that 9 but copy everything else down as -is.

Answer 14

Oh, you're finished with the previous problem and starting a new one? Sorry, I misunderstood.

Answer 15

Yes, I am now trying to find

4^x = 10, solve for x

Answer 16

I see you want to solve 4^x = 10 for x.

That 4^x is an exponential function with base 4, isn't it?

Answer 17

Can't remember, but you and I have probably talked about how the exponential function and the logarithmic function are inverses of each other. Do you recall that?

Answer 18

I used a pogram to help me solve this, nd this is the answer I got:

log(2) + log(5)
------------
2log(2)



I plugged it in and it was true, but I have to find a decimal and round to the nearest thousandths.

Answer 19

My point, Ricky, is that if you take the (log to the base 4) of both sides of 4^x = 10,

you'll end up with x = (log to the base 4) of 10.

Answer 20

So would the answer I need be x = 1.6610 ?

Answer 21

Please explain how you got that. Did you take the log to the base 4 of 10? If you can assure me that you did, then your answer is right. you should check it.

Answer 22

Yes, and I checked it and it all checks out!

Answer 23

Cool! Congratulations! It's great that you know the change of base formula.
Ricky, I'd be glad to continue, but it's taken longer than I expected to finish helping the other student. Please start on a new problem; post it; do your best to get started and then tell me what y ou ne3ed to know next.

Answer 24

Chosen a new problem yet?