1. logs and what not

Solve for x using logs. Give an exact answer.

35= 400e^(-0.4x)
Could someone point me in the right direction? Applying the logs to e is what's confusing me...

and then finding the inverse function of this problem...

f(t)=77e^(0.2t)

any help is greatly appreciated

2. 35= 400e^(-0.4x)?

Using logarithm to the base e,

ln (35) = ln (400) + ln (e^-0.4x)

ln (35) = ln 20^2 + (-0.4x) ln (e); [where ln e = 1]

ln (35) = 2 ln (20) - 0.4x

0.4x = 2 ln (20) - ln (35)

x = [2 ln (20) - ln (35)]/0.4 = 6.0903