Final answer:
The student's question about converting a logarithmic equation to exponential form is a high school level mathematics problem. The key property to use is that if a = log_b(c), then c = b^a, letting us rewrite the equation as (x+4)^(x+2) = x² - 5x + 9 and applying logarithmic identities as needed.
Step-by-step explanation:
The question involves rewriting a logarithmic equation as an exponential equation. Specifically, the student is given a logarithmic equation log_(x+4)(x²-5x+9)=x+2 and is seeking to convert it into its exponential form.
To convert the logarithmic equation to an exponential equation, we use one of the properties of logarithms: if a = log_b(c), then c = b^a. In the given equation, the base is (x+4) and the exponent is (x+2).
Therefore, we can express the equation in its exponential form as (x+4)^(x+2) = x² - 5x + 9.
Let's revise another important logarithmic identity: the product rule of logarithms, which states that log(xy) = log(x) + log(y), and the power rule, which says that log(x^y) = y*log(x).
These properties are key in working with logarithmic and exponential equations.