Math Problem Statement
Use the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient of 1 . All exponents should be positive.
ln(z)−ln(9)
Solution
We can condense the expression using the properties of logarithms. Specifically, we can apply the logarithm subtraction property, which states:
In your case, the expression is:
Using the logarithmic subtraction property, we can combine the two logarithms:
Thus, the condensed expression is:
This is the final simplified form, with a coefficient of 1, and no negative exponents.
Would you like to explore more logarithmic properties or have any questions? Here are some related topics for you:
- How to use the logarithm power rule: .
- The relationship between natural logarithms and exponents.
- How to apply logarithms to solve exponential equations.
- The change of base formula for logarithms.
- How to combine multiple logarithmic expressions with different bases.
Tip: Always remember that logarithms turn multiplication and division into addition and subtraction, which can make expressions easier to simplify!
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Math Problem Analysis
Mathematical Concepts
Logarithms
Logarithmic Properties
Formulas
ln(a) - ln(b) = ln(a/b)
Theorems
Logarithmic Subtraction Property
Suitable Grade Level
Grades 9-11