Question

What is the solution to log3(x+12)=log3(5x)

Answer 1

㏒3 (x+12)=㏒3 (5x)
㏒3(x+12)-㏒3(5x)=0
㏒3
`(x+12)/(5x)`=0

`3^(0) = (x+12)/(5x) ,`
1=(x+12)/5x
5x=x+12
5x-x=12
4x=12
x=12/4=3

Answer 2

Answer: The solution is x = 3.

Step-by-step explanation: We are given to solve the following logarithmic equation:

`\log 3(x+12)=\log 3(5x).`

We will be using the following property of logarithm:

`(i)~\log(ab)=\log a+\log b\\\\(ii)~\log a=\log b~~~\Rightarrow a=b.`

We have

`\log 3(x+12)=\log 3(5x)\\\\\Rightarrow \log3+\log(x+12)=\log 3+\log 5x\\\\\Rightarrow \log(x+12)=\log 5x\\\\\Rightarrow x+12=5x\\\\\Rightarrow 5x-x=12\\\\\Rightarrow 4x=12\\\\\Rightarrow x=3.`

Thus, the solution of the given equation is x = 3.