Find x.

5^x+ 5^x–1 = 750

Given: 5^x+ 5^x–1 = 750

We know that, when the bases of the terms are same and those terms are multiplied, then their exponents are added.

⇒ 5^x + 5^x ×5^-1 = 750

By taking 5^x from above equation, we get,

5^x (1 + 5^-1) = 750

As when the bases of the terms are same and those terms are divided, then their exponents are subtracted.

⇒ 5^{x – 1} = 5³

As the bases are same so the exponents can be equated,

⇒ x – 1 = 3

⇒ x = 4