(11)
4e^x - 4 = 2 divide through by 2
2e^x - 2 = 1 add 2 to both sides
2e^x = 3 divide both sides by 2
e^x = 3/2 = 1.5 take the ln of both sides
ln e^x = ln 1.5 and we can write
x * ln e = ln 1.5 and ln e = 1, so we can ignore this
x = ln 1.5 ≈ .4055
(12)
10 + 5e^(2x) = 17 subtract 10 from both sides
5e^(2x) = 7 divide by 5 on each side
e^(2x) = 7/5 = 1.4 take the ln of both sides
lne^(2x) = ln1.4 and we can write
(2x) * lne = ln 1.4 and ln e = 1, so we can ignore this
2x = ln 1.4 divide by 2
x = [ln 1.4 ] / 2 ≈ .168