Finding Intersection Points of Exponential Functions

Very Hard Passport To Advanced Math Exponential Functions

Consider the function defined by the equation:

$$f(x) = 3^{2x} - 5 $$

and let $$g(x) = 5^{x-1}. $$

What is the value of $$x$$ such that $$f(x) = g(x)$$?

Express your answer in terms of logarithms.

$$x = rac{1}{2} ext{log}_5{8} + 1$$

$$x = rac{1}{4} ext{log}_5{72}$$

$$x = ext{log}_5{5} + 1$$

$$x = rac{2 ext{log}_5{3} + 1}{2}$$

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