Question

Find the solution to the equation log16 32 = x + 2. (4 points)

Part 2: Using complete sentences, explain the procedure used to solve this equation. (4 points)

Answer 1

Hint: Do you know how to remove the base-16 logarithm from the left-hand-side of the equation?

Answer 2

32 = 16^(x + 2)

Note that 32 = 2^5 and 16 = 2^4. Then,

2^5 = 2^(4(x + 2))
2^5 = 2^(4x + 8)

Set the exponents = to each other and solve for x:

5 = 4x + 8
4x = 5 - 8
4x = -3
x = -3/4