Step 1: Start with the equation log_3(x) + log_3(4) = 2.
Step 2: Use the property of logarithms that says log_a(b) + log_a(c) = log_a(b*c).
Step 3: Combine the logs: log_3(x * 4) = 2.
Step 4: Rewrite the equation in exponential form: x * 4 = 3^2.
Step 5: Calculate 3^2, which is 9: x * 4 = 9.
Step 6: Solve for x by dividing both sides by 4: x = 9 / 4.
Step 7: Simplify 9 / 4 to get x = 2.25.
Logarithmic Properties – The question tests the understanding of properties of logarithms, specifically the product rule which states that log_b(a) + log_b(c) = log_b(ac).
Exponential Equations – It also tests the ability to convert logarithmic equations into exponential form to solve for the variable.
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