Question

solve log x base 2 +
log(x+6) base 2= 4​

Answer 1

Answer:

x = 2

Step-by-step explanation:

Given :

㏒₂ x + ㏒₂ ( x + 6 ) = 4

Using ㏒ property :

㏒ m + ㏒ n = ㏒ ( m . n )

= > ㏒₂ ( x . ( x + 6 ) ) = 4

We can write 4 as 4 ㏒₂ 2 :

= > ㏒₂ ( x² + 6 x ) = 4 ㏒₂ 2

= > ㏒₂ ( x² + 6 x ) = ㏒₂ 2⁴

Comparing both side we get :

= > x² + 6 x = 16

= > x² + 6 x - 16 = 0

= > x² + 8 x - 2 x - 16 = 0

= > x ( x + 8 ) - 2 ( x + 8 ) = 0

= > ( x + 8 ) ( x - 2 ) = 0

= > x = - 8 OR x = 2

We know ㏒ is defined for only positive number i.e. :

If ,

㏒ₓ a = α

= > x > 0 , a > 0 and x ≠ 1

Therefore , the required answer is x > 0 i.e. x = 2

Hence we get required answer!

Answer 2

X= -8,2

Properties usages

1.base change

2.logx+logy=log(xy)

3logx=logy

=x=y