Final answer:
To find the largest value of x that satisfies log₂(x²) - log₂(x + 3) = 7x, first combine the logs into a single logarithm and rewrite the equation as an exponential equation. Then, isolate x and use numerical methods or a graphing calculator to determine the value.
Step-by-step explanation:
We need to find the largest value of x that satisfies the equation: log₂(x²) - log₂(x + 3) = 7x.
First, apply the properties of logarithms to combine the logs into a single logarithm: log₂(x² / (x + 3)) = 7x.
By the definition of a logarithm, this equation can be rewritten as an exponential equation: x² / (x + 3) = 2^(7x).
Solve this equation for x by isolating x and then use numerical methods or a graphing calculator to find the largest value that satisfies the equation.