Final answer:
To solve the equation 6³ˣ⁻³=36ˣ⁺³, rewrite the bases as (2²)³ˣ⁻³=(6²)ˣ⁺³. Simplify to (2⁶ˣ⁻³)=(6⁶ˣ⁺³), and equate the exponents to solve for x. The resulting equation has no solution.
Step-by-step explanation:
To solve the equation 6³ˣ⁻³=36ˣ⁺³, we need to get the bases on both sides of the equation to be the same. In this case, we can rewrite 6³ˣ⁻³ as (2²)³ˣ⁻³, and 36ˣ⁺³ as (6²)ˣ⁺³.
Now we have (2²)³ˣ⁻³=(6²)ˣ⁺³. We can simplify this to (2⁶ˣ⁻³)=(6⁶ˣ⁺³), since we can raise both sides of an equation to the same power without changing their relative values.
Finally, we can solve for x by equating the exponents: 6x - 3 = 6x + 3. By subtracting 6x from both sides, we get -3 = 3, which is not true. Therefore, there is no solution for the given equation.