If 2m=4x and 2w = 8x, what is m in terms of w?

Explanation

To determine m in terms of w, we first rewrite the equations with the same base.Given: 2^m = 4x 2^w = 8xConvert 4x and 8x into powers of 2: 4x = 2^2 * x 8x = 2^3 * xDivide the two equations: (2^m) / (2^w) = (4x) / (8x)Simplify the right side: (4x) / (8x) = 1/2So: 2^(m - w) = 1/2Write 1/2 as a power of 2: 1/2 = 2^(-1)Thus: m - w = -1Therefore: m = w - 1Other options (w + 1, 2w - 1, and 2w + 1) suggest incorrect relationships as they imply different mathematical connections between m and w based on the original equations.