Solve the equations: 3^x+9^x+27^x=−7

Question

asked Jul 23, 2019 170k views

2 Answers

Klamann · Answer 1 · 2019-07-29T21:53:36+0000

I would love to solve this equation but unfortunately, it has no solution

the reason it has no solution is that that we want raise positive numbers to a certain power to get a negative number

note that
$a^b\geq 0$ when a≥0 and b is a real number

let's say that 3ˣ=a, 9ˣ=b, and 27ˣ=c

therefore, since
$3^x\geq 0$ ,
$9^x\geq 0$ , and
$27^x\geq 0$ , a≥0, b≥0, and c≥0

also, a+b+c≥0 by logic

if
3^x+9^x+27^x=a+b+c and
3^x+9^x+27^x=-7 and a+b+c≥0 and then we get
$-7 \geq 0$ which is a false statement

therefore, there is no real solution