Question

How do you solve `log 3x=log 4+log (x-3)`?

Answer 1

`x=12`

Explanation:

`1`. Use the log property, `log_color(purple)b(color(red)m*color(blue)n)=log_color(purple)b(color(red)m)+log_color(purple)b(color(blue)n)` to simplify the right side of the equation.

`log(3x)=log4+log(x-3)`

`log(3x)=log(4(x-3))`

`log(3x)=log(4x-12)`

`2`. Since the equation now follows a "`log=log`" situation, where the bases are the same on both sides, rewrite the equation without the "log" portion.

`3x=4x-12`

`3`. Solve for `x`.

`3x-4x=-12`

`-x=-12`

`color(green)(|bar(ul(color(white)(a/a)x=12color(white)(a/a)|)))`