SOLUTION: Solve where appropriate 43=4e^3x

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve where appropriate 43=4e^3x      Log On


   

Question 328530: Solve where appropriate
43=4e^3x
Found 2 solutions by nyc_function, Alan3354:
Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
Isolate the exponential expression by dividing both sides by 4.
43 = 4e^(3x)
43/4 = e^(3x)
Now take the natural log of both sides of the equation.
Let ln = natural log
ln(43/4) = ln[e^(3x)]
ln(43/4) = 3xlne
We now solve for x. To do so, divide both sides by lne.
ln(43/4) divided by lne = x
NOTE: lne = 1 by definition
ln(43/4) divided by 1 = x
ln(43/4) = x
2.374905755 = x
Round to the nearest tenths.
So, x is approximately 2.4

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
43=4e^3x
e^3x = 43/4 = 10.75
3x = ln(10.75)
x = ln(10.75)/3