Solve for x

Problem

(log_3)(x2)=2*(log_3)(4)−4*(log_3)(5)

Solution

1. Apply the power property of logarithms to the right side of the equation, which states n*(log_b)(a)=(log_b)(an)

(log_3)(x2)=(log_3)(4)−(log_3)(5)

2. Simplify the exponents inside the logarithms.

(log_3)(x2)=(log_3)(16)−(log_3)(625)

3. Apply the quotient property of logarithms to the right side, which states (log_b)(a)−(log_b)(c)=(log_b)(a/c)

(log_3)(x2)=(log_3)(16/625)

4. Equate the arguments of the logarithms since the bases are the same.

x2=16/625

5. Solve for x by taking the square root of both sides.

x=±√(,16/625)

6. Simplify the square root to find the final values.

x=±4/25

Final Answer

(log_3)(x2)=2*(log_3)(4)−4*(log_3)(5)⇒x=±4/25

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