Question

log(x+2)+log(x-2)=log5​

Answer 1

Answer:

Your question isn't clear enough for an answer. I don't know whether if u are asking to prove the logarithmic equation or find 'x'.

So, I assumed that you want to find the value of x .

=> x = +3

Step-by-step explanation:

log(x−2)+log(x+2)=log5

∴log(x−2)(x+2)=log5....(loga.b=loga+logb)

∴x^2−4=5

∴x^2−9=0

∴x=±3

Since x>2, x will be equal to 3.

OR

LOG ( (x+2)(x-2)) = log 5

(x+2)(x-2) = 5

x^2 - 4 = 5

x^2 - 9 = 0

(x+3)(x-3)=0

x= -3 or x = 3

The solution x=-3 results in the log of a negative number,

and negative numbers are NOT in the domain of the log function.

The solution x=3 checks out! log(3+2) + log (3-2) = log(5) + log(1) = log(5) + 0 = log(5)

So x=3.

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(I gave u three examples of methods of the same thing. Hope it helps.(◍•ᴗ•◍)❤)