Use natural logarithmics to solve the equation round to the nearest thousandth 3e^2x +5=26

x = 0.973

3e^(2x) +5 = 26

3e^(2x) = 21 . . . . . subtract 5

e^(2x) = 7 . . . . . . . divide by 3

2x = ln(7) . . . . . . . .take the natural log

x = ln(7)/2 ≈ 0.973 . . . . divide by 2 and evaluate

x= .973

Step-by-step explanation:

3e^2x +5=26

Subtract 5 from each side

3e^2x +5-5=26-5

3e^2x =21

Divide by 3 on each side

3/3e^2x =21/3

e^2x =7

Take the natural log on both sides

ln (e^2x) =ln (7)

2x = ln (7)

Divide by 2

2x/2 = ln(7)/2

x = ln(7)/2

x is approximately .972955075

Rounding to the nearest thousandth

x = .973

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