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1. Solve $\displaystyle 3\ e^{4x-5}=2$Originally Posted by Lane
Divide through by $\displaystyle 3$ to get:
$\displaystyle e^{4x-5}=2/3$
Now take natural logs of both sides:
$\displaystyle
4x-5=\log_e(2/3)
$.
Add $\displaystyle 5$ to both sides:
$\displaystyle
4x=\log_e(2/3)+5
$,
finally divide through by $\displaystyle 4$:
$\displaystyle
x=(\log_e(2/3)+5)/4 = \log_e \left(\root {1/4}\of {2/3} \right) + 5/4
$
RonL