Question

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

Answer 1

Answer:

X=2/5

Step-by-step explanation:

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

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

logm+logn=logmn

log5x(2x+3)=log10(3-x) power2

log10xsquare+15x=log10(9+xsquare-6x)

loga=logb then a=b

10x square+15x=10xsquare+30-60x

10x square is cancelled

15x+60x=30

75x=30

x=2/5

I think this is your required answer

Answer 2

Given :

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

To find : x

Identity used :

• log a + log b = log (a×b)

• log 10 = 1

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

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

Solution :

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

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

=> 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)

=> x = (6/5) = 1.2

ANSWER : x = (6/5) = 1.2