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Find all solutions of the equation below.

5^(3x-2)=2
The solution(s) is/are
x=◻
◻
(Simplify your answer. Use a comma to separate answers as needed. Round to four decimal places as needed.)

Find all solutions of the equation below. $\newline$ $5^{3 x-2}=2$ $\newline$ The solution(s) is/are $x=\square$ $\newline$ (Simplify your answer. Use a comma to separate answers as needed. Round to four decimal places as needed.)

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Complex conjugate theorem

Full solution

Q. Find all solutions of the equation below.

\newline

5^{3 x-2}=2

\newline

The solution(s) is/are

x=\square

\newline

(Simplify your answer. Use a comma to separate answers as needed. Round to four decimal places as needed.)

Take Logarithm: Take the logarithm of both sides to simplify the equation; using the natural logarithm ( $\ln$ ) is common for such problems.
Apply Power Rule: Apply the power rule of logarithms, which states $\ln(a^b) = b\cdot\ln(a)$ , to simplify the left side.
Isolate $x$ : Solve for $x$ by isolating it on one side of the equation. First, divide both sides by $\ln(5)$ .
Add $2$ : Add $2$ to both sides to further isolate the term with $x$ .
Divide by $3$ : Finally, divide everything by $3$ to solve for $x$ .

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