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If log_10(1000) = x, what is the value of x?
Practice Questions
Q1
If log_10(1000) = x, what is the value of x?
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Questions & Step-by-Step Solutions
If log_10(1000) = x, what is the value of x?
Steps
Concepts
Step 1: Understand that log_10(1000) means 'to what power do we raise 10 to get 1000?'
Step 2: Rewrite 1000 as a power of 10. We know that 1000 = 10^3.
Step 3: Now, substitute this back into the logarithm: log_10(1000) = log_10(10^3).
Step 4: Use the property of logarithms that says log_b(b^a) = a. Here, b is 10 and a is 3.
Step 5: Therefore, log_10(10^3) = 3.
Step 6: Conclude that x = 3.
Logarithms
– Understanding the relationship between exponents and logarithms, specifically how to evaluate logarithms with base 10.
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