Question

How do you solve `Log (x-1) + Log 2 = Log (3x)`?

Answer 1

There is no solution for `x`.

Explanation:

By the laws of logarithms, `loga + logb = log(a*b)`.

Using this law:
`log(x-1)+log2 = log(3x)`
`log(2(x-1)) = log(3x)`

Using the distributive property (`a*(b+c) = ab + ac`):
`log(2x -2) = log(3x)`

`10^(log(2x-2)) = 10^log(3x)`
`2x-2 = 3x`
`3x = 2x -2`
Subtracting `2x` from both sides:
`x = -2`

Since you can not apply `log` on a negative number, there is no solution for this equation.