Question

Please help me.
2 ^ (2x - 3) * .5 ^ (x - 1) = 200
​

Answer 1

x = 3

Explanation:

`{2}^((2x - 3)) \ast {5}^((x - 1)) = 200 \\ \\ \implies \: {2}^((2x - 3)) \ast {5}^((x - 1)) =8 \ast \: 25 \\ \\\implies \: {2}^((2x - 3)) \ast {5}^((x - 1)) = {2}^(3) \ast {5}^(2)`

Comparing like terms on both sides, we find:

`{2}^((2x - 3))= {2}^(3)\: \: or \:\:{5}^((x - 1)) = {5}^(2)`

`\implies \:2x - 3 = 3 \: \: or \: \:x - 1 = 2 \\ \\ \implies \:2x = 3 + 3 \: \: or \: \: x = 1 + 2\\ \\ \implies \:2x = 6 \: \: or \: \: x = 3 \\ \\ \implies \:x = (6)/(3) \: \: or \: \: x = 3 \\ \\ \implies \:x = 3 \: \: or \: \: x = 3 \\ \\ \implies \huge \:x = 3`