Math Problem Statement
³log54+³log18-³log 12
Solution
To simplify the expression:
We use the logarithmic properties:
- Logarithm of a product:
- Logarithm of a quotient:
Let’s simplify step by step.
-
Combine the first two logarithms using the product rule:
-
Now subtract :
-
Since , the logarithm becomes:
Thus, the value of the given expression is:
Would you like more details on any specific step?
Here are some related questions:
- How does the change of base formula apply to logarithms?
- Can you explain other properties of logarithms, like the power rule?
- How would the result change if the logarithm base was different?
- What are the common applications of logarithms in real-life problems?
- How can we express logarithms in terms of natural logs?
Tip: Always remember to simplify logarithmic expressions step by step using product and quotient rules first!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Logarithms
Logarithmic Properties
Simplification
Formulas
Logarithm of a product: log_a(xy) = log_a x + log_a y
Logarithm of a quotient: log_a(x/y) = log_a x - log_a y
Theorems
Logarithmic Properties
Suitable Grade Level
Grades 10-12
Related Recommendation
Logarithmic Expression Simplification: 3log 54 + 3log 18 – 3log 12
Simplify Logarithmic Expression log 54 + log 18 - log 12
Simplifying Logarithmic Expression: 4 Log 54 + 3 Log 18 - 3 Log 12
Simplify Logarithmic Expression: 3Log 54 + 3Log 18 - 3Log 12
Solve Logarithmic Expression: log 54 + log 18 - log 12