Question

`log_24 + log_216 - log_232`

Answer 1

Answer: 1

Explanation:

Method #1: Using the log rules (+ → x and - → ÷)

log₂4 + log₂16 - log₂32

= log₂
`((4*16)/(32))`

= log₂
`((64)/(32))`

= log₂2

= 1

Method #2: Using log rules to simplify each expression

log₂4 = x log₂16 = x log₂32 = x

4 = 2ˣ 16 = 2ˣ 32 = 2ˣ

2² = 2ˣ 2⁴ = 2ˣ 2⁵ = 2ˣ

2 = x 4 = x 5 = x

log₂4 = 2 log₂16 = 4 log₂32 = 5

2 + 4 - 5 = 1