Natural logarithms are useful because they help express many relationships in the physical world.
Space A spacecraft can attain a stable orbit 300 km above Earth if it reaches a velocity of 7.7 km/s. The formula for a rocket's maximum velocity v in kilometers per second is
Let
How can you solve the problem?
Use the given formula to find the maximum velocity v of the spacecraft. If
The maximum velocity of 8.0 km/s is greater than the 7.7 km/s needed for a stable orbit. Therefore, the spacecraft can attain a stable orbit 300 km above Earth.
Write each expression as a single natural logarithm.
Solve each equation.