Solve the equation `log_10 x^2 = log_10x + log_ 10 4`

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

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.

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