Question

Solve the equations: 3^x+9^x+27^x=−7

Answer 1

The answer would be No Solution, because the equation is unsolvable without an x value.

Answer 2

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