[tex]Solution, \mathrm{Inverse\:of}\:2^x+6:\quad \frac{\ln \left(x-6\right)}{\ln \left(2\right)}[/tex]
[tex]Steps:[/tex]
Definition [tex]If\;a\;function\;f\left(x\right)\;s\;mapping\;x\;to\;y,\;then\;the\;inverse\;function\;of\;f\left(x\right)\;maps\;y\;back\;to\;x.[/tex]
[tex]y=2^x+6[/tex]
[tex]\mathrm{Interchange\:the\:variables}\:x\:\mathrm{and}\:y, x=2^y+6[/tex]
[tex]\mathrm{Solve}\:x=2^y+6\:\mathrm{for}\:y, y=\frac{\ln \left(x-6\right)}{\ln \left(2\right)}, \frac{\ln \left(x-6\right)}{\ln \left(2\right)}[/tex]
The correct answer is [tex]\frac{\ln \left(x-6\right)}{\ln \left(2\right)}[/tex]
Hope this helps!!!
<3 -austint1414
