Question

What is the true solution to the logarithmic equation below?

Answer 1

Option c

Explanation:

The given logarithmic equation is

`log_(2) (6x)-log_(2)(√(x))=2`

`log_(2)[((6x))/(√(x))]=2` [since log
`((a)/(b))`= log a - log b]

`log_(2)[((6√(x))*√(x))/(√(x))]=2` [since x =
`(√(x))(√(x))`]

`log_(2)(6√(x) )=2`

`6√(x) =2^2` [logₐ b = c then
`a^(c)=b`

`6√(x) =4`

`√(x) =(4)/(6)`

`√(x) =(2)/(3)`

`x=((2)/(3))^2`

=
`(4)/(9)`

Option c is the answer.

Answer 2

x = 4/9

C

Explanation:

log_2(6x/) - log_2(x^(1/2) = 2 Given

log_2(6x/x^1/2) = 2 Subtracting logs means division

log_2(6 x^(1 - 1/2)) = 2 Subtract powers on the x s

log_2(6 x^(1/2) ) = 2 Take the anti log of both sides

6 x^1/2 = 2^2 Combine the right

6 x^1/2 = 4 Divide by 6

x^1/2 = 4/6 = 2/3 which gives 2/3 now square both sides

x = (2/3)^2

x = 4/9