Find the solution of the exponential equation , correct to four decimal places. e^(-4x) = 6

We'll recall the principle
that:

e^a = b <=> a = ln
b

For the given equation, we'll take logarithms both
sides:

ln e^(-4x) = ln 6

We'll apply
the power property of logarithms:

ln e^a = a*ln
e

-4x*ln e = ln 6

But ln e =
1.

-4x = ln 6

We'll divide by -4 both
sides:

x = -ln 6/4

We'll get the
calculator to find ln 6 = 1.7917

x =
-1.7917/4

The solution of x, rounded to four decimal places,
is:

x = -0.4479