Question

Solve for x? 2^x+6 = 5^x-2

Answer 1

Just to clarify, the + 6 and -2 are not in the exponent, right? because if they are you need parentheses

Answer 2

Oh yes. Sorry. They are in the exponent. I'll remember that for future reference. Thank you so much.

Answer 3

It's been a while for me on logs so give me a sec

Answer 4

Oh sure. That's quite fine. I just appreciate the help. :)

Answer 5

so the question is \[\huge 2^{x+6} = 5^{x-2}\]right?

Answer 6

I'll give this one to Igb

Answer 7

nahh i just wanted to do some latex

Answer 8

Yep, that's right. :) Thanks.

Answer 9

So how would I go about solving it?

Answer 10

\[\Large 2^{x+6} = 5^{x-2}\]
take the log of both sides
\[\Large \log 2^{x+6} = \log 5^{x-2}\]
use power rule
\[\Large(x+6) \log 2 = (x-2) \log 5\]
isolate x
\[\Large \frac{x+6}{x-2} = \frac{\log 5}{\log 2}\]
use change of base formula
\[\Large \frac{x+6}{x-2} = \log_2 5\]
now solve log_2 5

Answer 11

Thanks for the help. So how would I solve the next portion of this? I really don't know how to do this one at all. :(

Answer 12

you. solve3. log_2 5. like. i. said.

Answer 13

nevermind that 3 there. it's a typo

Answer 14

Alright. So would it be 1.505149978?

Answer 15

hmm no...

Answer 16

what did your calculator tell you about \[\log 5 \div \log 2\]

Answer 17

I tried putting that into my calculator now. Is it 2.321928095?

Answer 18

yes. so \[\frac{x+6}{x-2} \approx 2\]
\[\implies x + 6 \approx 2(x-2)\]
\[\implies x + 6\approx 2x - 4\]
\[\implies 4 + 6 \approx 2x - x\]
\[\implies 10 \approx x\]
do you follow that?

Answer 19

I think so. So, the answer is 10 then? Or is there more to this problem?

Answer 20

as far as im concerned.. i'd like it to be 10 period. although..it is a little inaccurate since you did logarithms but heh

Answer 21

my answer comes out to be 0.398

Answer 22

Thank you for your help too. Is that the answer you got too Igbasallote?