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If log_3(x) + log_3(4) = 2, find x.
If log_3(x) + log_3(4) = 2, find x.
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Practice Questions
1 question
Q1
If log_3(x) + log_3(4) = 2, find x.
1
4
9
12
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log_3(4x) = 2 => 4x = 3^2 = 9 => x = 9/4 = 2.25.
Questions & Step-by-step Solutions
1 item
Q
Q: If log_3(x) + log_3(4) = 2, find x.
Solution:
log_3(4x) = 2 => 4x = 3^2 = 9 => x = 9/4 = 2.25.
Steps: 7
Show Steps
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.
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