How do you solve 3+e^(2x+1)=10

3 + e^(2x+1) = 10

e^(2x+1) = 7

ln [e^(2x+1)] = ln 7

2x + 1 = 1.9459

2x = 0.9459

x = 0.473


Hope this helps...good luck!

3 + e^(2x+1) = 10
e^(2x+1) = 7
2x + 1 = ln(7)
2x = ln(7) - 1
x = (.5)[ln(7) -1]

ln represents the natural log function.

3+e^(2x+1)=10
e^(2x+1)=7
ln(e^2x+1)=ln(7)

Ln is the natural logarithm (log base e). ln(e^y) always equals y.
Thus:
2x+1=ln(7)
x=(ln(7)-1)/2
x=0.473


Check:
3+e^(0.473*2+1)=10
3+7=10
Correct.

3+(e^(2x+1)) = 10
e^(2x + 1) = 7
ln(e^(2x + 1)) = ln( 7)
ln cancels out e....so

2x + 1 = ln(7)
2x = ln(7) - 1
x = (ln(7) - 1) / 2

e^(2*x + 1) = 7

ln(e^(2*x + 1)) = ln(7)

2*x + 1 = 1.945910149

x = 0.4729550745