7-6 Solving Natural Log Equations
Natural Logs. Define: Natural Logarithm – a logarithm with
base “e”You solve natural logs the same way as any
other log. SOLVE 53ln x
32)2ln(4 x
53ln ee x 8)2ln( x
53 ex
3
5ex 47.49
8)2ln( ee x
96.29802x96.2978x
Solving exponential equations with base “e” 1624 2 xe
122 xe
12lnln 2 xe
485.22x
485.4x
5.32 xe5.3lnln 2 xe
253.12 x
6264.0x
144 2 xe
A spacecraft can only attain a stable orbit 300 km above the earth if it reaches a velocity of 7.7 km/s. Suppose a rocket has a mass ratio (R) of 25, a firing time (t) of 100 s and an exhaust velocity (c) of 2.8 km/s. Use the formula below to find if the spacecraft attain a stable orbit 300 km above the earth’s surface? Rctv ln0098.0
25ln8.2)100(0098.0 v)219.3(8.298.0 v
0.8v
The spacecraft can attain a stable orbit 300km above earth, since the max velocity 8.0km/s is greater than the 7.7km/s needed.
PracticePg 481 # 11-13, 20-22, 31-35 odd, 38, 39
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