Math Problem Statement
Solution
The problem in the image asks to find the value of the following expression:
We can simplify this using the properties of logarithms:
- Logarithm Addition:
- Logarithm Subtraction:
Step-by-step solution:
-
Combine the logarithms that are added:
-
Combine the subtraction:
-
Lastly, add :
Since , the final value is:
The value of the expression is 4.
Would you like further details or clarifications?
Here are five related questions for further practice:
- What is the value of ?
- How do the properties of logarithms simplify expressions involving multiple logarithms?
- What is the value of ?
- How do you convert logarithms with different bases?
- How do logarithmic properties relate to exponential functions?
Tip: When working with logarithms, remember the properties of logarithms (product, quotient, and power rules) as they are useful in simplifying complex expressions.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Logarithms
Algebra
Properties of Logarithms
Formulas
log_b(x) + log_b(y) = log_b(x * y)
log_b(x) - log_b(y) = log_b(x / y)
Theorems
Properties of Logarithms
Suitable Grade Level
Grades 10-12
Related Recommendation
Calculate Logarithmic Expression ²log 4 + ²log 10 - ²log 5
Simplify log_2(24) - log_2(8) + log_2(20) Using Logarithmic Rules
Simplifying Logarithmic Expressions: log 4 log 40 + log 5 log 16
Simplify Logarithmic Expression log(10)(40) + log(10)(2.5)
Simplifying Logarithmic Expression: 3 log 4 + log 5 - log 40