Question

If 4a^+9b^=37ab,what is the value of 2log(2a-3b)

Answer 1

Step-by-step explanation:

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Answer 2

The value of $2\log(2a-3b)$ $=2\log 5+\log a+\log b$.

Step-by-step explanation:

We have,

$4a^2+9b^2=37ab$

To find,  the value of $2\log(2a-3b)$ = ?

∴ $2\log(2a-3b)$

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

Using the logarithm identity,

$\log a^n=n \log a$

$=\log (4a^2+9b^2-12ab)$

Using algebraic identity,

$(a-b)^{2} =a^{2} +b^{2} -2ab$

$=\log (37ab-12ab)$

$=\log (25ab)$

$=\log 25+\log a+\log b$

$=2\log 5+\log a+\log b$

Thus, the value of $2\log(2a-3b)$ $=2\log 5+\log a+\log b$.