Question

log5x +log (2x + 3) = 1 + 2.log(3-x)                x < 3 ​

Answer 1

Explanation:

Solution:

log5x +log (2x + 3) = 1 + 2.log(3-x)

log5x + log(2x + 3) = log10 + log(3-x)2

log(5x.(2x +3)) = log (10.(3-x)2)

5x.(2x +3) = 10.(3-x)2

10x2 +15x = 10.(9-6x + x2)

10x2 + 15x = 90-60x +10x2

75x = 90

Answer 2

✮ Question ✮

log5x +log (2x + 3) = 1 + 2.log(3-x)  

Answer :-

$\therefore\underline{\boxed{\textsf{x = {\textbf{6/5}}}}} \qquad\qquad \bigg\lgroup\bold{Required \ answer} \bigg\rgroup$

Given :

log5x +log (2x + 3) = 1 + 2 log(3-x)    x < 3

Have To find

Value of x .

Calculations :-

As we know that ;-

log a + log b = log (a×b)

log 10 = 1

$\sf \: log( {a}^{m} ) \: = m \: log(a)$

$\sf \: if \: log(a) = log(b) \implies \: a = b$

Hence , just applying the identity :-

↠ log 5 x +log ( 2x + 3 ) = 1 + 2 log ( 3-x )    

↠ log { ( 5x ) (2x + 3 ) }= log 10 + log ( 3-x )²

Here we use one more identity =

( a - b )² = a² + b² - 2ab .

↠ log { ( 5x ) ( 2x + 3 ) } = log ( 10 ×( 3 - x )² )

↠ 5x ( 2x + 3 ) = 10× ( 3 - x )²

↠ 10x² + 15x = 10 × ( 9 + x² - 6x)

↠ 10x² + 15x = 90 + 10x² - 60x

↠ 10x² - 10x² + 15x + 60x = 90

↠ 75x = 90

↠x = 90 / 75

$\large{\boxed{\bold{x\:=\:6/5}}}$