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