Given the logarithmic equation:
log₉(x² + 4x + 22) = 2x,
we can convert this to an exponential equation. In logarithms, the base of the logarithm can also transfer as the base of an exponential. The result of the logarithm equates to the power in the exponential form, and the number inside the logarithm becomes the result in the exponential form.
Therefore, the base here is 9.
To convert to an exponential form, we can write it as:
base^(logarithm) = argument,
where the base is 9, the logarithm is 2x, and the argument is the expression inside the logarithm i.e., x² + 4x + 22.
Hence, the exponential form of the given logarithmic equation will be:
9^(2x) = x² + 4x + 22.