Math Problem Statement
Find value of x X[log3-log10]=(1-x) long20
Solution
The equation you provided is:
To solve for , follow these steps:
Step 1: Expand the logarithms
We can simplify the equation by recalling that:
Thus, the equation becomes:
Step 2: Isolate
Now, expand the equation to distribute and :
Move all terms involving to one side:
Factor out :
Step 3: Solve for
Finally, solve for :
Step 4: Simplify the equation
Recognize that is . Substitute this back into the equation:
This expression gives you the value of .
Would you like me to calculate the exact numerical value of , or do you have any questions about the steps?
Follow-up Questions:
- How do logarithmic properties help simplify complex equations?
- What are the key differences between natural logarithms and common logarithms?
- How can logarithms be applied in solving exponential growth problems?
- Can you explain the relationship between logarithms and exponents?
- What are the practical applications of logarithms in real-world scenarios?
Tip:
Always remember that logarithmic identities are powerful tools for simplifying complex expressions, especially in equations involving products or ratios.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Equations
Solving Equations
Formulas
Logarithm properties
Exponential equations
Theorems
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Suitable Grade Level
Advanced High School