Solve: [tex]e^{6x} = 6e^{x}[/tex]
Taking the natural log of both sides will cancel out the left hand side, since exponentials and logarithmic functions are inverses of each other.
[tex]ln(e^{6x}) = ln(6e^{x})[/tex]
Using the property, log(ab) = log(a) + log(b), we can simplify the right hand side, and the left side simply will cancel down to 6x.
[tex]6x = ln(6) + ln(e^{x})[/tex]
[tex]6x = ln(6) + x[/tex]
Isolate the variable to solve directly for x.
[tex]6x - x = ln(6)[/tex]
[tex]5x = ln(6)[/tex]
[tex]\therefore x = \frac{ln(6)}{5}[/tex]
