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What is the value of x if log×5+log6b =log192+logb?
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What is the value of x if log×5+log6b =log192+logb?
Understanding the Equation
To solve the equation log(x)5 + log(6)b = log(192) + log(b), we start by using the properties of logarithms.
Step 1: Combine the Logarithms
- We can combine the logarithmic expressions using the property log(a) + log(b) = log(ab).
- Thus, the left side becomes: log(5x) + log(6b) = log(30xb).
- The right side becomes: log(192b).
Step 2: Set the Arguments Equal
- Since the logarithm function is one-to-one, we can set the arguments equal to each other:
- 30xb = 192b.
Step 3: Simplify the Equation
- Assuming b ≠ 0, we can divide both sides by b:
- 30x = 192.
Step 4: Solve for x
- Now isolate x:
- x = 192 / 30.
- Simplifying gives: x = 64 / 10 = 6.4.
Final Value of x
- Therefore, the value of x is 6.4.
Conclusion
- By applying logarithmic properties and algebraic manipulation, we determined that x = 6.4.
To solve the equation log(x)5 + log(6)b = log(192) + log(b), we start by using the properties of logarithms.
Step 1: Combine the Logarithms
- We can combine the logarithmic expressions using the property log(a) + log(b) = log(ab).
- Thus, the left side becomes: log(5x) + log(6b) = log(30xb).
- The right side becomes: log(192b).
Step 2: Set the Arguments Equal
- Since the logarithm function is one-to-one, we can set the arguments equal to each other:
- 30xb = 192b.
Step 3: Simplify the Equation
- Assuming b ≠ 0, we can divide both sides by b:
- 30x = 192.
Step 4: Solve for x
- Now isolate x:
- x = 192 / 30.
- Simplifying gives: x = 64 / 10 = 6.4.
Final Value of x
- Therefore, the value of x is 6.4.
Conclusion
- By applying logarithmic properties and algebraic manipulation, we determined that x = 6.4.
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What is the value of x if log×5+log6b =log192+logb?
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What is the value of x if log×5+log6b =log192+logb? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about What is the value of x if log×5+log6b =log192+logb? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value of x if log×5+log6b =log192+logb?.
What is the value of x if log×5+log6b =log192+logb? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about What is the value of x if log×5+log6b =log192+logb? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value of x if log×5+log6b =log192+logb?.
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