Given:
The logarithmic equation is:

To find:
The value of x.
Solution:
Properties of logarithm used:


is defined for
.
We have,

Using properties of logarithm, we get
![\log [x(x-3)]=\log 10](https://img.qammunity.org/2022/formulas/mathematics/high-school/7wwb8sw22tlv0r3mjsb3qmvbsrkc1bp6w2.png)

Splitting the middle term, we get




In the given equation, we have a term
. It means the value of x must be greater than 0 or positive. So, the only possible value of x is:

Therefore, the value of x is 5.