A bit rusty on the ln's.
1.5=ke^3k.
attempt
ln1.5=3klne
ln1.5=3k(1)
(ln1.5)/3=k???
Thanks....
you have k as a coefficient of the exponential term and k as part of the exponent. An elementary algebraic approach to solve for k is not available ... you'll need to use technology.
let $\displaystyle k = x$
graph $\displaystyle y = xe^{3x} - 1.5$ and locate any zeros ...
$\displaystyle x = k = 0.4224126...$