3e^2x=18
x=6/e^2
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3e^2x=18
e^2x = 6
2x = ln6
x = 1/2 ln6
To solve the equation 3e^(2x) = 18, we would follow these steps:
Step 1: Divide both sides of the equation by 3 to isolate the exponential term:
(3e^(2x))/3 = 18/3
e^(2x) = 6
Step 2: Take the natural logarithm (ln) of both sides to eliminate the exponential:
ln(e^(2x)) = ln(6)
2x ln(e) = ln(6)
Since ln(e) equals 1, we can simplify this to:
2x = ln(6)
Step 3: Divide both sides of the equation by 2 to solve for x:
(2x)/2 = ln(6)/2
x = ln(6)/2
Therefore, the solution to the equation 3e^(2x) = 18 is x = ln(6)/2.