Question

log(x+3) +log(x-3) =log27​

Answer 1

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We have given log function both sides so,we apply logorithm identity here to solve this type of Questions

=>log(x+3)+log(x-3)=log27

On the left side there is variable and on the other side there is constant inside log.So, it's difficult to solve without using any logorithm property.

We know that : logm + logn= logmn

The function on the left side is in the form of logm+logn

So, log (x+3)+log(x-3)= log(x+3)(x-3)

=>log(x+3)(x-3)= log27

Here,we see that log on both sides so,log will be cancelled

=>(x+3)(x-3)= 27

Here ,(x+3)(x-3) is the form of identity (a+b)(a-b)

Identity used here :

(a+b)(a-b)=a²-b²

=>x²-3²=27

=>x²-9=27

=>x²=27+9=36

=>x=√36

=>x=6

Extra information=>

Some other logorithm properties:

• logm-logn= logm÷long
• value of log1=0
• logbase e will be considered as 1