Question

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

Answer 1

`x=5`

Explanation:

Use Properties: `log_b(xy)=log_b x+log_by`

`log_bx=y iff b^y=x`

`log (x(x-3))=1` `color(white)(xxxxxx)` [ 1 = log10]

`log(x^2-3x)=log10`

`x^2-3x^1 = 10^1`

`x^2-3x-10=0`

`(x-5)(x+2)=0`

`x=5 or x=-2`