Question

Hello everyone , I need help in this one : \[\large{\frac{2^x}{1+2^x}=\frac{1}{4}}\] , then the value of \[\large{\frac{8^x}{1+8^x}}\]

Answer 1

is that second part related to the first part?

Answer 2

I am getting upto this step : \(\large{2^{x+2}=1+2^x}\)

Answer 3

yes may be lemme try that also @lgbasallote

Answer 4

may I say something? :

I am not getting the one that I should have..

Answer 5

I got this... may be I made this more complex..

Answer 6

what if in the first part you let

a = 2^x

\[\implies \frac{a}{1+a} = \frac 14\]
cross multiply
\[\implies 4a = 1 + a\]
subtract a from both sides
\[\implies 3a = 1\]
divide both sides by 3
\[\implies a = \frac 13\]
sub back a = 2^x
\[\implies 2^x = \frac 13\]
use log
\[\implies \log_2 (\frac 13) = x\]
does that help?

Answer 7

is there any involvement of log.. in the first expression? (eqn)

Answer 8

hmn right I will use this wait

Answer 9

If you didn't see that method, you can also go this way.\[2^{x+2}-2^x=1\]\[2^x(4-1)=1\]\[2^x=\frac{1}{3}\]

Answer 10

right I am doing that .. kg sir

Answer 11

Oh k so i got \(\frac{1}{28}\)

Answer 12

it's in option and is right..

also the process is excellent

thanks to both @lgbasallote and @KingGeorge

Answer 13

You're welcome.

Answer 14

oh..cool...it was a questionception

Answer 15

:)

Answer 16

btw can any1 tell me that these type of questions come into which topic?

Answer 17

Basic algebra or exponents ? something like that