Find the value of 𝑥 for which five-sixths to the power of four 𝑥 minus two is equal to twenty-five thirty-sixths.
We notice that 25 is equal to five squared and 36 is equal to six squared. This means that we can rewrite the right-hand side of our equation as five-sixths squared. This is equal to five-sixths to the power of four 𝑥 minus two. And we notice that the base on both sides is the same. We can, therefore, conclude that the exponents must also be equal. Four 𝑥 minus two must equal two. Adding two to both sides of this equation gives us four 𝑥 is equal to four. And we can then divide both sides of this equation by four, giving us 𝑥 is equal to one.
The value of 𝑥 for which five-sixths to the power of four 𝑥 minus two is equal to twenty-five thirty-sixths is one. We could check this answer by substituting 𝑥 equals one into the left-hand side of the original equation. Four multiplied by one minus two is equal to two, and five-sixths squared is equal to twenty-five thirty-sixths.