Question: If log_2(x) + log_2(4) = 6, what is the value of x?
Options:
8
16
32
64
Correct Answer: 32
Solution:
log_2(x) + 2 = 6 implies log_2(x) = 4, so x = 2^4 = 16.
If log_2(x) + log_2(4) = 6, what is the value of x?
Practice Questions
Q1
If log_2(x) + log_2(4) = 6, what is the value of x?
8
16
32
64
Questions & Step-by-Step Solutions
If log_2(x) + log_2(4) = 6, what is the value of x?
Step 1: Start with the equation: log_2(x) + log_2(4) = 6.
Step 2: Recognize that log_2(4) is equal to 2 because 2^2 = 4.
Step 3: Substitute 2 for log_2(4) in the equation: log_2(x) + 2 = 6.
Step 4: To isolate log_2(x), subtract 2 from both sides: log_2(x) = 6 - 2.
Step 5: Simplify the right side: log_2(x) = 4.
Step 6: Convert the logarithmic equation to exponential form: x = 2^4.
Step 7: Calculate 2^4, which equals 16.
Step 8: Therefore, the value of x is 16.
Logarithmic Properties – Understanding how to manipulate logarithmic equations, including the use of the property that log_b(a) + log_b(c) = log_b(a*c).
Exponential Equations – Solving for x by converting logarithmic equations into exponential form.
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