Question

List the potential solutions to 2log x − log3 = log3 from least to greatest.

x = ? Or... x = ?

Please explain the steps

Answer 1

remember
if no base is stated, assume base 10
and

`log_a(b)=c` translates to
`a^c=b`
and

`log(a)+log(b)=log(ab)`
and

`log(a)-log(b)=log((a)/(b))`
and

`(r)log(x)=log(x^r)`

so

minus log3 from both sides

2log(x)-2log(3)=0
translate

`log(x^2)-log(3^2)=0`
translate

`log((x^2)/(9))=0`
translate

`10^0=(x^2)/(9)`

`1=(x^2)/(9)`
times both side by 9
9=x²
+/-3=x



x=-3 or 3