Answer:
[tex]y=\log_3(x)[/tex]
Step-by-step explanation:
[tex]3^y=x[/tex]
[tex]\ln(3^y)=\ln(x)[/tex]
[tex]y\ln(3)=\ln(x)[/tex]
[tex]y=\frac{\displaystyle\ln(x)}{\displaystyle\ln(3)}[/tex]
but if
[tex]f(x)=\frac{\displaystyle\ln(x)}{\displaystyle\ln(3)}[/tex]
then since
[tex]f(3)=\frac{\displaystyle\ln(3)}{\displaystyle\ln(3)}=1[/tex]
[tex]f(x)=\log_3(x)[/tex]
so
[tex]y=\log_3(x)[/tex]
or
[tex]3^y=x[/tex]
[tex]\log_3(3^y)=\log_3(x)[/tex]
[tex]y\log_3(3)=\log_3(x)[/tex]
[tex]\text{but }\,\log_3(3)=1, \text{so,}[/tex]
[tex]y=\log_3(x)[/tex]
