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

The value of x is 5 , - 5

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)</strong></p><p>[tex]Log_(2)`(x + 3) +
`Log_(2)`(x - 3) =
`Log_(2)( (x + 3) × (x - 3) )</p><p> [tex]Log_(2)( (x + 3) × (x - 3) ) = 4</p><p>Again </p><p> [tex]Log_(a)b = x</p><p>So , <strong>b = [tex]a^(x)`

So, (x + 3) × (x - 3) =
`2^(4)`

Or, x² - 9 = 16

or, x² = 25

∴ x =
`√(25)`

I.e x =
`\pm` 5

Hence the value of x is 5 , - 5 Answer