Question

The steps to solve it. Unsure what step I am missing.

solve: e^(6x)=6e^(x)

Answer 1

Solve:
`e^(6x) = 6e^(x)`

Taking the natural log of both sides will cancel out the left hand side, since exponentials and logarithmic functions are inverses of each other.


`ln(e^(6x)) = ln(6e^(x))`

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.


`6x = ln(6) + ln(e^(x))`

`6x = ln(6) + x`

Isolate the variable to solve directly for x.

`6x - x = ln(6)`

`5x = ln(6)`


`\therefore x = (ln(6))/(5)`