Question

☺PLEASE ANSWER THE QUESTION.

LOGARITHMIC EQUATION.

$log(5) \: + \: log(x + 10) - 1 = \\ log(21x - 20) - log(2x - 1)$

Answer 1

Given Equation is log(5) + log(x + 10) - 1 = log(21x - 20) - log(2x - 1).

We know that log(a) + log(b) = log ab.

= > log(5(x + 10)) -  1 = log(21x - 20) - log(2x - 1)

= > log(5(x + 10)) - 1 + log(2x - 1) = log(21x - 20)

We know that log(10) = 1

= > log(5(x + 10)) - log(10) + log(2x - 1) = log(21x - 20)

= > log(5(x + 10) + log(2x - 1) = log(21x - 20) + log(10)

We know that log a + log b = log ab

= > log(5(x + 10) * (2x - 1)) = log((21x - 20) * log 10)

= > 5(x + 10)(2x - 1) = (21x - 20 ) * 10

= > 5(2x^2 - x + 20x - 10) = 210x - 200

= > 5(2x^2 + 19x - 10) = 210x - 200

= > 10x^2 + 95x - 50 = 210x - 200

= > 10x^2 + 95x + 150 = 210x

= > 10x^2 - 115x + 150 = 0

= > 5(2x^2 - 23x + 30) = 0

= > 2x^2 - 23x + 30 = 0

= > 2x^2 - 20x - 3x + 30 = 0

= > 2x(x - 10) - 3(x - 10) = 0

= > (2x - 3)(x - 10) = 0

= > x = 3/2, 10.



Hope this helps!

Answer 2

Hi,

Please see the attached file!

Thanks