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.
$6x - x = ln(6)$
$5x = ln(6)$

$\therefore x = \frac{ln(6)}{5}$