Question

Square root of a equals cube root of b. For what value does a^(2x-1) = b?

a. x = 1/2
b. x = 1
c. x = 2
d. x = 3

Answer 1

To find the value of x for which a^(2x-1) = b, given that the square root of a equals the cube root of b, we set the exponents equal and solve for x, resulting in x = 1.

Step-by-step explanation:

The question asks us to find the value of x for which a2x-1 = b, given that square root of a equals cube root of b. Let's solve this step by step.

First, express 'a' and 'b' in terms of their roots:

• a = (√a)2
• b = (∛b)3

Based on the given equation, (√a)2 = (∛b)3 which suggests that:

• a = b

This means for a2x-1 to be equal to b, we must have:

• a2x-1 = a

Hence, the exponent on 'a' must be 1. To find the value of x that makes this true, set the exponents equal:

• 2x - 1 = 1
• 2x = 2
• x = 1

Therefore, the correct answer is x = 1, which corresponds to option b.