Question

7.
The solution x of the equation log4(3x + 7) - log4(x - 5) = 2 satisfy ?
​

Answer 1

The solution of x = 87/13 for the equation.

We have to find the solution of x for the equation, log₄(3x + 7) - log₄(x - 5) = 2.

Here, log₄(3x + 7) - log₄(x - 5) = 2

we know from logarithmic rule,

$log_a(m)-log_a(n)=log_a(mn)$

⇒log₄(3x + 7) - log₄(x - 5) = log₄ [(3x + 7)/(x - 5)] = 2

⇒log₄[(3x + 7)/(x - 5)] = 2

from logarithmic rule,

$log_a(m)=N\implies m=a^N$

⇒[(3x + 7)/(x - 5)] = 4² = 16

⇒(3x + 7) = 16(x - 5)

⇒3x + 7 = 16x - 80

⇒16x - 3x = 80 + 7

⇒13x = 87

⇒x = 87/13

For log to be defined, (3x - 5) > 0 and (x - 5) > 0

so, x > 5 here, x = 87/13 > 5

Therefore value of x = 87/13