Question

Find the base of y = b^x that contains the point (3/2, 27)

Answer 1

Answer:

• D) b = 9

Step-by-step explanation:

Given function:

• y = b^x

The graph of it should contain the point (3/2, 27)

Substitute the values and verify answer choices:

A) b= 3/2

• 27 = (3/2)^(3/2), False as the right side is irrational

B) b= 27

• 27 = 27^(3/2), False as 27^1 ≠ 27^(3/2), because 1 ≠ 3/2

C) b= x/y

• 27 = (x/y)^(3/2), False as is doesn't make sense

D) b= 9

• 27 = 9^(3/2)
• 27 = (3^2)^(3/2)
• 27 = 3^(2*3/2)
• 27 = 3^3
• 27 = 27