Question

Two numbers, a and b, are each greater than zero, and the square root of a is equal to the cube root of b. For what value of x is a^(2x-1) equal to b ?

Answer 1

Answer:

x = 1/2

Step by step explanation:

Two numbers a and b are each greater than zero.

i.e a > 0 and b > 0

And;

$\sqrt{a} \: = \: \sqrt[3]{b}$

Since the square root of a is equal to cube root of b then,

a = b = 1

${a}^{2x \: - \: 1} \: = \: b$

${1}^{2x \: - \: 1} = {1}^{0}$

2x - 1 = 0

x = 1/2