If (2a-3b)= a- b, then a=

Correct Answer is : 3b22b−1{3b²}{2b-1}2b−13b2

Correct Answer is : 3b22b−1{3b²}{2b-1}2b−13b2

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Logarithms

Question : 50 of 85

Marks: +1, -0

\log (2a-3b)=\log a-\log b

a=

Solution:

Concept:

Use the property

\log a - \log b = \log \frac{a}{b}

and equate arguments.

Explanation:

Given:

\log (2a-3b) = \log a - \log b

Using log property:

\log a - \log b = \log \frac{a}{b}

So,

\log (2a-3b) = \log \frac{a}{b}

Since logs are equal,

2a-3b = \frac{a}{b}

Multiply both sides by

b

b(2a-3b) = a

⇒

2ab - 3b^2 = a

Rearrange:

2ab - a = 3b^2

⇒

a(2b-1) = 3b^2

Thus,

a = \frac{3b^2}{2b-1}

Answer:

a = \frac{3b^2}{2b-1}

, which matches option A.

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