A Quick And Easy Exponential Equation

[@RyanLewis-Johnson-wq6xs]

(2^4+2^4)/(4^4+4^4+4^4)=1/24 x=4 0.001(41.6 recurring)=1/24 solution

[@andylee3114]

I only saw the substitution approach. Nice to see there is at least one other way to do it.

[@gelbkehlchen]

Solution:
(2^x+2^x)/(4^x+4^x+4^x) = 1/24
2*2^x/(3*2^x*2^x) = 1/24 |*3/2 ⟹
1/(2^x) = 1/16 |*16*2^x ⟹
2^x = 16 = 2^4 |because of the same base ⟹ x = 4

[@cyruschang1904]

2^x = y, 4^x = y^2
24(2y) = 3y^2
16 = y
x = 4

[@Lucerd127]

Same

[@cyruschang1904]

@@Lucerd127 🙂

[@NilestienRamaeuler]

can u solve underoot x+underoot-x=2....find all complex solutions and verify

[@giuseppemalaguti435]

2a/3a^2=1/24..2/3a=1/24...a=16..x=4

[@bkkboy-cm3eb]

2^x = u
→ 2u/3u²=1/24
u=16 → 2^x=16 ∴x=4

[@rakenzarnsworld2]

x = 4

[@scottleung9587]

I also got x=4 as the only solution.

[@nasrullahhusnan2289]

1/24=2×2^x/[3×(2²)^x]
=2×2^x/[3×(2^x)²]
24(2×2^x)=3×(2^x)²
16(2^x)=(2^x)²
(2^x)[(2^x)-16]=0 --> 2^x=2⁴
x=4

[@juergenilse3259]

(2^x+2^x)/(4^x+4^x+4^x)=1/24
(2*2^x)/(3*4^x)=1/24
(2*2^x)/(3*(2^2)^x)=1/24
2/3+(2^x/(2^2)^x=1/24
(2/3)*(3/2)*2^x/(2^2)^x=(3/2)*(1/24)
1*2^x/2^2x=3/48=1/16
2^x/2^2x=1/2^4
2^(x-2x))=2^(--4)
2^(--x)=2^(-4)
-x=--4
x=4