Answer: x = 2/3
Step-by-step explanation:
log₂(x) + log₂(2x) + log₂(3x) + log₂(36) = 6
According to the following properties of logarithm, we know that:
logₐ(x.y) = logₐ(x) + logₐ(y)
logₐ(x) = n
logₐ(x) = logₐ(y) ⇔ x = y
Applying this properties to the situation:
log₂(x.2x.3x.36) = log₂64
log₂(216x³) = log₂64
216x³ = 64
x³ = 64/216
x³ = 8/27
x = 2/3
