Question

Solve the exponential equation.
9^8x = 27
I don't understand how to solve this. If you know I will give medal (:
A) 5/8
B) 3/16
C) 9
D) 16/3

Answer 1

hint take logarithns

Answer 2

Hint: rewrite both the 9 and the 27 as powers of 3:\[(3^{2})^{8x}=3^{3}\]
since y ou now have the same base on both sides, it's easy to solve for x. Try it. If the resulting x doesn't match any of your answers, double check to ascertain that you've copied the problem down correctly.

Answer 3

so the logarithm would look like this right? log8^27 = x

Answer 4

or you can convert as follows
- i was just going to do what mathmale has just written

Answer 5

alright. I will solve and then tell you what I got. Then you or mathmale will tell me if I'm right.

Answer 6

no

8x *log 9 = log 27

Answer 7

If you, usernae, choose to use logs to solve this problem for x, you'd end up with

8x log 9 = log 27. Solve for x.

Answer 8

so do I divide log 9 from log 27 in order to be left with x. Then simplify from there?

Answer 9

Yes, that's an appropriate approach. Then you'll need to isolate x.

Answer 10

my answer is x = 3/8

Answer 11

Please check that result by substitution.

Answer 12

no thats not the answer
show us your working

Answer 13

I divided log27/log9

Answer 14

x should be = [log 27 / log 9] / 8

Answer 15

then I isolated the x by dividing both sides by 8

Answer 16

right so far

Answer 17

yep

Answer 18

but that's not one of the answer choices. However, when I plugged in the logarithm into wolfram it gave me 3/16. Where did the 16 come from? Do you know?

Answer 19

what did you get log 27 / log 9?

Answer 20

yes I did (:

Answer 21

If
\[9^{8x}=27,\]
\[(3^{2})^{8x}=3^{3}\]
is also true. Then 16x=3, and x = ???

Answer 22

Logs should also lead to the correct answer.

Answer 23

log27/lgo9 = 3/2

divide this by 8 gives 3/2 * 1/8 = 3/16

Answer 24

I advocated this particular solution some time ago, but read it incorrectly and tried to solve 6x=3 for x, whereas it should be 16x=3.

Answer 25

but wait. 27/9 = 3.

Answer 26

While 27/9=3, you are actually dividing (log 27) by (log 9).

Answer 27

you need to divide the logs not the numbers

log 27 / log 9 = 1.5 or 3/2

Answer 28

And that 's not 3.

Answer 29

ohhh okay then. I get it now. so the answer is 3/16. Thank you @cwrw238! and thank you mathmale! Listen if it's not too much, I have one more question.

Answer 30

Post it separately, please!