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If log(2a-3b)=log a -log b, then a=
Most Upvoted Answer
If log(2a-3b)=log a -log b, then a=
Log(2a-3b)= log a - log b
log (2a - 3b) = log (a/b)
2a - 3b = a/b
b(2a - 3b) = a
2ab - 3b^2 = a
2ab - a = 3b^2
a (2b - a) = 3b^2
a = 3b^2 / (2b - a)
Community Answer
If log(2a-3b)=log a -log b, then a=
Explanation: Solving for a given equation
We are given an equation log(2a-3b)=log a -log b, and we are required to solve for a. Here is how we can do it:
Step 1: Simplify the equation
We can simplify the equation using the following logarithmic identities:
- log a - log b = log (a/b)
- log x + log y = log (xy)
Using these identities, we can rewrite the equation as:
- log(2a-3b) = log (a/b)
- 2a-3b = a/b
Step 2: Rearrange the equation
We can rearrange the equation to isolate a on one side:
- 2a - 3b = a/b
- 2ab - 3b^2 = a
- a = 3b^2 / (2b-1)
Step 3: Check for extraneous solutions
Since we took the logarithm of both sides of the original equation, we need to check if the solution we obtained is valid. If a or b is negative or zero, then the logarithm is undefined.
Step 4: Final answer
The final answer is:
- a = 3b^2 / (2b-1), where b > 1/2 and b ≠ 0
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If log(2a-3b)=log a -log b, then a= for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If log(2a-3b)=log a -log b, then a= covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log(2a-3b)=log a -log b, then a=.
If log(2a-3b)=log a -log b, then a= for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If log(2a-3b)=log a -log b, then a= covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log(2a-3b)=log a -log b, then a=.
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