Question

6 exponent 1 minus x is equal to 6 exponent 2x

Answer 1

To solve
`6^(1-x)`=
`6^(2x)`, you need to understand a very important exponent rule.

When two bases are the same, you are allowed to treat the exponents as their own separate equations!

The bases on both sides of the equation are 6, so you can treat 1-x and 2x as separate equations. Set them equal to each other and solve for x.

`1-x=2x`

* add x to both sides*

`1=3x`

*divide 3 from both sides*

`(1)/(3)=x`

To check your answer, plug in
`(1)/(3)` where you see x in the original equation. You will see that you will be left with
`6^{1-(1)/(3) }` =
`6^(2x)`, which equals
`6^{(2)/(3) } = 6^{(2)/(3) }`