Solve to 2 decimal places: 438=200e^0.25x the answer is x=3.14 Please explain how?

Como2016-05-07T13:06:25Z

438/200 = e^(x/4)
ln [ 438/200 ] = x/4
x = 4 ln [ 438/200 ]
x = 3 • 14

DWRead2016-05-07T13:20:16Z

First put parentheses around the exponent.
438 = 200e^(0.25x)
e^(0.25x) = 438/200 = 2.19

take natural log of both sides
ln(e^(0.25x)) = ln(2.19)
0.25x = ln(2.19) ≅ 0.784
x = 4·0.784 ≅ 3.14

lenpol72016-05-07T13:27:02Z

438 = 200 e^(0.25x)

Divide both sides by '200'
Hence
2.19 = e^(0.25x)

Take log to base 'e' ( ln)
ln 2.19 = ln e^(0.25x)
0.7839 = (0.25x) ln e

NB ln e = 1
Hence
0.7839 = 0.25x
x = 0.7839/0.25
x = 3.1356....
Hence x = 3.14 ( to nearest hundredth).

TopCat2016-05-07T12:44:19Z

438=200e^0.25x
438/200=e^0.25x
2.19=e^0.25x
ln(2.19)=ln(e^0.25x)
ln(2.19)=0.25x
x=ln(2.19)/0.25
x=3.14