Math Problem Statement
Condense the complex logarithm into single term log(x + 1)^2 + log(2x - 1)^3 - log(x)^2 - log(2x - 1)^4 + 6log(x + 1)
Solution
To condense the given complex logarithm into a single term, we will use the properties of logarithms. Specifically, we will use the product rule, quotient rule, and power rule of logarithms.
The expression is:
-
Apply the power rule of logarithms to bring the exponents in front of the logarithms:
-
Combine like terms: Simplify the coefficients:
-
Use the product rule of logarithms to combine the terms into a single logarithm:
-
Use the quotient rule of logarithms to condense the expression further:
So, the condensed form of the given logarithmic expression is:
Would you like more details on this solution, or do you have any further questions?
Here are 5 questions you might want to ask next:
- How do you expand a single logarithmic term into multiple terms?
- What are the common properties of logarithms and how are they used in solving equations?
- Can you provide an example of solving a logarithmic equation step by step?
- How do you solve logarithmic inequalities?
- What are some real-world applications of logarithmic functions?
Tip: Practice combining and condensing logarithmic expressions using the product, quotient, and power rules to become more comfortable with simplifying complex logarithmic equations.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Logarithms
Properties of Logarithms
Logarithmic Equations
Formulas
Power rule of logarithms
Product rule of logarithms
Quotient rule of logarithms
Theorems
-
Suitable Grade Level
High School
Related Recommendation
Condense Logarithmic Expression: log₃ 6 + 2·log₃ x + 1/2 log₃ 9
Simplify log x + log y - 2 log z to a Single Logarithm
Simplifying Logarithmic Expression: 2log6 4 + 3log6 x - 4log6 y
Simplifying Logarithmic Expression: 4log(x) - 4log(x^2 + 1) + 3log(x - 1)
Condensing Logarithmic Expressions 5[4 ln(x) − ln(x + 1) − ln(x − 1)]