If 8x-1 = \(\frac{1}{4}\), find x

If 8^x-1 = \(\frac{1}{4}\), find x

Answer Details

We know that 8^x-1 = \(\frac{1}{4}\). We can write 8^x-1 as (2³)^x-1 = 2^3x-3. Similarly, we can write 1/4 as 2^-2. Therefore, we can write the given equation as 2^3x-3 = 2^-2. Since the bases are equal, we can equate the exponents to get: 3x - 3 = -2 Adding 3 to both sides, we get: 3x = 1 Dividing both sides by 3, we get: x = \(\frac{1}{3}\) Therefore, the value of x is \(\frac{1}{3}\).