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What is the value of log_10(1000) + log_10(0.01)?
What is the value of log_10(1000) + log_10(0.01)?
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What is the value of log_10(1000) + log_10(0.01)?
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log_10(1000) = 3 and log_10(0.01) = -2, thus 3 - 2 = 1.
Questions & Step-by-step Solutions
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Q: What is the value of log_10(1000) + log_10(0.01)?
Solution:
log_10(1000) = 3 and log_10(0.01) = -2, thus 3 - 2 = 1.
Steps: 5
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Step 1: Understand that log_10(x) means 'to what power must 10 be raised to get x'.
Step 2: Calculate log_10(1000). Since 10^3 = 1000, we find that log_10(1000) = 3.
Step 3: Calculate log_10(0.01). Since 10^-2 = 0.01, we find that log_10(0.01) = -2.
Step 4: Add the two results together: 3 (from log_10(1000)) + (-2) (from log_10(0.01)).
Step 5: Simplify the addition: 3 - 2 = 1.
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