Question

i need some help solving for x

2^(x+1) + 8^(x-2) = 24

answer is 3 using trial and error, however, i need the solution.

thank you in advance!

Answer 1

as 8 = 2^3 we can rewrite the expression as:
\[2^{x+1}+2^{3(x-2)}=24\]
Then taking \[\log _{2}\]
of both sides we get:
\[\log _{2}(x+1) + \log _{2}(3x-6) = \log_{2}24\]

Answer 2

another thing, we are not allowed to use log...

Answer 3

ahhhh. that is unfortunate

Answer 4

24 = 16 + 8
24 = 2^4 + 2^3
2^(x+1)+2^(3x−6)=2^4 + 2^3

Answer 5

x+1 = 4
3x-6 = 3

Answer 6

Those both solve to
x=3
and x = 3

Answer 7

yup - good work

Answer 8

got the answer already

Answer 9

it's the same with TBates! thank you!