Question

Solve for x:
$\log (x+3) + \log (x-3) = \log 16$

Answer 1

Answer:

5

Step-by-step explanation:

Hi,

We will be using the following properties of  

logarithm:

Additive Property : logₐx + logₐy = logₐ(xy) ,

Subtraction Property : logₐx - logₐy = logₐ(x/y)and

and Power 0 Property : log 1 = 0 or if log x = 0 then x = 1

Given that log ( x + 3) + log ( x - 3) = log 16

Using Additive Property, we can write as

log (x + 3)*(x - 3) = log 16

log (x² - 9 ) = log 16

log (x² - 9) - log 16 = 0

Using Subtraction Property

log [(x² - 9)/16] = 0

Thus,

x² - 9/16 = 1

x² - 9 = 16

x² = 25

x = ± 5

But, x cannot be - 5, since logarithm is defined only for

positive numbers.

Hence, x = 5

Hope, it helps !