Question

What is the solution to the equation 9^-3x ≈ 7 ?

Answer 1

are you there?

Answer 2

Yes.

Answer 3

what class is this for? if any

Answer 4

Algebra II

Answer 5

are you doing logarithms?

Answer 6

Yes.

Answer 7

is it multiple choice?

Answer 8

Yes.

Answer 9

x=\[\frac{ \log(7) }{ 6 \log(3) }\] is this one of your answer choices?

Answer 10

x = -0.295
x = -0.376
x = 0.376
x = 0.295

Answer 11

@iplayffxiv, what kind of website do you think this is? A site where you help students understand how to do the problem or a site where you just give the answer?

Answer 12

Do you know how to do this, Hero?

Answer 13

uhhh a site where u help people understand............

Answer 14

@celecity, yes, I know how to do it.
@iplayffxiv, how should I classify what you have done here? Giving help or giving answers?

Answer 15

Would you mind walking me through it?

Answer 16

uhhhhh i dont know.............

Answer 17

why dont you tell me

Answer 18

Well, @iplayffxiv, I don't see where you explained any concepts or gave any general formulas, or defined anything or presented any postulates or anything related to general problem solving. All I see that you've posted is a possible answer choice.

Answer 19

Anyway, @celecity,

\[9^{-3x} \approx 7\]

Answer 20

Or more explicitly,

\[9^{(-3x)} \approx 7\]

Answer 21

Anytime you see a negative exponent, it translates to the multiplicative inverse of the given expression. Therefore we can re-write the expression as the inverse of \(9^{3x}\). Doing that will give us:

\[\frac{1}{9^{3x}} \approx 7\]

Answer 22

Now, there's a particular rule we can use to simplify the expression in the denominator:

\(a^{(bc)} = (a^{b})^c\)

Answer 23

So \(9^{3x} = (9^3)^x\) or simply \(729^x\)

Answer 24

Replacing that in the denominator, we have:

\[\frac{1}{729^x} = 7\]

Answer 25

Now, since we are trying to isolate x, let's write this in a more convenient manner. Muliply both sides by \(729^x\) and divide by sides by 7 to get:

\[\frac{1}{7} = 729^x\]

Do you think you might be able to solve it from here?

Answer 26

Hint: Taking logs of both sides is involved.

Answer 27

So that would be log1/7=log729?

Answer 28

What did you do with the x?

Answer 29

Remember, there was an x in the exponent before you logged both sides. What did you do with it?

Answer 30

It would be =log729^x

Answer 31

Right?

Answer 32

Then after logging both sides, what will the resultant equation be?

Answer 33

The log1/7 results in -0.84509804 and the log729^x is 28.62727528

Answer 34

Remember \(\log a^x = x \log(a)\)

Answer 35

Oh, okay, one moment.

Answer 36

-0.84509804 = x(2.862727528)

Answer 37

I think you might know what the next step is in order to isolate x. What does x equal?

Answer 38

-0.2952072916

Answer 39

Is that one of your answer choice?

Answer 40

-0.295 is. Thank you so much for your help :)

Answer 41

yw