Final answer:
To solve the exponential equation y = 9ˣ for x, take the base 9 logarithm of both sides to get log₉(y) = x, which isolates x as the solution.
Step-by-step explanation:
The student's question involves solving an exponential equation for the unknown variable. Specifically, we need to isolate x in the equation y = 9ˣ. To do this, we apply logarithms. Assuming y is known, we take the base 9 logarithm of both sides of the equation to isolate x:
log₉(y) = log₉(9ˣ)
Since log₉(9ˣ) is simply x (because any number raised to the power of its base's logarithm equals the exponent), the equation simplifies to:
log₉(y) = x
This is how we solve for x given an exponential function of the form y = 9ˣ.