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polet [3.4K]
3 years ago
14

28. Solve for x.

Mathematics
1 answer:
bija089 [108]3 years ago
5 0

Answer:

The value of x is 5 , - 5

Step-by-step explanation:

Given as :

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

Now, <u>from log property</u>

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) ) = 4Again  [tex]Log_{a}b = xSo , 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

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