The equation to be solved is: `log_10x^2 = log_10 x + log_10 4`
Use the property of logarithm log a + log b = (a*b)
`log_10 x^2 = log_ x + log_ 4`
=> `log_ x^2 = log_ 4*x`
=> `x^2 = 4x`
=> `x^2 - 4x = 0`
=> `x(x - 4) = 0`
=> x = 0 and x = 4
But log 0 is not defined.
The solution of the equation is x = 4
I suggest you to isolate the logarithmic terms containing x to the left side, keeping only constant term to the right such that:
`log (x^2) - log x = log 4`
Using the quotient property of logarithmic function yields:
`log ((x^2)/x) = log 4 =gt log x = log 4 ` => x = 4
This approach helps you to avoid the indetermination created by the root x=0 that you may get if you keep the logarihmic terms containing x both sides.
Hence, the solution to equation is x=4.