The solution to equation [tex]324=4(3)^{2x}[/tex] is x = 2.
What is exponential function?
An exponential function is a mathematical function of the following form:
[tex]f(x) = a^{x}[/tex]. where x is a variable, and a is a constant called the base of the function.
Given exponential equation
[tex]324=4(3)^{2x}[/tex]
[tex]4(3)^{2x}=324[/tex]
[tex]3^{2x} =\frac{324}{4}[/tex]
[tex]3^{2x}=81[/tex]
[tex]3^{2x}=3^{4}[/tex]
When bases are equal, power should be equal.
2x = 4
x = 2
Hence, the solution to equation [tex]324=4(3)^{2x}[/tex] is x = 2.
Option C is correct.
Find out more information about exponential function here
https://brainly.com/question/14355665
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