Question

Если x0 корень уравнения log2x+log4x+log16x=7 то выражение√x0+2 равно

Answer 1

log₂x + log₄x + log₁₆x = 7

log₂x + 1/2 log₂x + 1/4 log₂x = 7

4/4 log₂x + 2/4 log₂x + 1/4 log₂x = 7

7/4 log₂x = 7

log₂x = 7 * 4/7

log₂x = 4

x = 2⁴ = 16

x₀ = 16

√x₀ + 2 = √16 + 2 = 4+2 = 6

ответ: 6