Question

Given that y=log_(2)x, find expressions in terms of y for
log₂x² (2)

Answer 1

The expression for log₂x²(2) in terms of y is 1 + y.

Step-by-step explanation:

Given that y = log₂x, we can substitute y into the expression log₂x²(2) to obtain:

log₂x²(2) = log₂(x² * 2)

Using the distributive property of logarithms, we can simplify the expression:

log₂x²(2) = log₂(x²) + log₂(2)

Since log₂x = y, we can substitute y into the expression:

log₂x²(2) = y + log₂(2)

The base of the logarithm is 2, so log₂(2) = 1. Substituting this value into the expression, we get:

log₂x²(2) = y + 1

Therefore, the expression for log₂x²(2) in terms of y is 1 + y.