Question

How do you solve `log (x – 2) + log x = log 3`?

Answer 1

Use the rules `log_an + log_am = log_a(n xx m)` and `log_an - log_am = log_a(n/m)`

Explanation:

Put all the logs on one side of the equation:

`log(x - 2) + logx - log3 = 0`

`log(((x + 2)x)/3) = 0`

`log((x^2 + 2x)/3) = 0`

Now, convert to exponential form. You are in base 10, since nothing is noted in subscript by the log.

`(x^2 + 2x)/3 = 10^0`

`(x^2 + 2x)/3 = 1`

`x^2 + 2x = 3`

`x^2 + 2x - 3 = 0`

`(x + 3)(x - 1) = 0`

`x = -3 and 1`

It is always vital to check your solutions after solving logarithmic equations. Neither solutions work, because the log of a negative number is undefined in the real number system. Therefore, this equation has no solution `(O/)`.

Hopefully this helps!