Question

28. Solve for x.
log 2(x + 3) + log 2(x - 3) = 4
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O
A. The solution(s) is/are x =
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B . The solution is not a real number
O
Solve for x

Answer 1

Answer:

The value of x is 5 , - 5

Step-by-step explanation:

Given as :

$Log_{2}$(x + 3) + $Log_{2}$(x - 3) = 4

Now, from log property

$Log_{b}m + [tex]Log_{b}n = [tex]Log_{b}(m × n)

[tex]Log_{2}$(x + 3) + $Log_{2}$(x - 3) = $Log_{2}( (x + 3) × (x - 3) )

[tex]Log_{2}( (x + 3) × (x - 3) ) = 4

Again

[tex]Log_{a}b = x

So , b = [tex]a^{x}$

So,  (x + 3) × (x - 3) = $2^{4}$

Or,  x² - 9 = 16

or,  x² = 25

∴  x = $\sqrt{25}$

I.e x = $\pm$ 5

Hence the value of x is 5 , - 5  Answer