Question

Log(2x+3)+log(2x-3)=log55.what will be the value of x?

Answer 1

If the base of both the logs are same , then
Log(2x+3)+Log(2x-3)=Log55
=>Log(4x²-9)=Log55
=>4x²-9=55
=>4x²-64=0
=>(2x+8)(2x-8)=0
Hence,
x=4. x= -4

Answer 2

Answer:

x= 4, -4

Step-by-step explanation:

Given : Expression $log(2x+3)+log(2x-3)=log55$

To find : The value of x

Solution :

If the base of both the logs are same, then

$log(2x+3)+log(2x-3)=log55$

Applying logarithmic property,$logA+logB=logAB$

$log(2x+3)(2x-3)=log55$

Applying property $(a+b)(a-b)=a^2-b^2$

$log(4x^2-9)=log55$

Since, the base is same we remove the the log

$4x^2-9=55$

$4x^2-64=0$

$(2x)^2-8^2=0$

$(2x+8)(2x-8)=0$

$2x+8=0\Rightarrow x=-4$

and $2x-8=0\Rightarrow x=4$

Hence,

x=4, x= -4