As increases from 1 to 10, the value of increases from ______ to ______. (Fill in the two blanks with numbers.)
Answer & Analysis
Analysis
Question Analysis
This question involves tracking the change in the value of the common logarithm as x increases between two specific values (1 and 10).
The main focus is on using basic logarithmic properties to find the function values at the endpoints of the interval.
Key Concept Explanation
For the common logarithm (base 10):
A core property is , because (any number to the power of 0 is 1).
Another key property is , because (a number to the power of 1 is itself).
Since is an increasing function (base 10 > 1), as x increases from 1 to 10, f(x) will increase from to .
Step-by-Step Solution
1. Find the value of when :
2. Use the property
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