[Type text]
P.o.D. – Solve each equation.
1.) log4x=log5+log4
2.) log6+log10=log(5a)
3.) log4h=12log449-log43
4.) log8x2=2log85+3log82
5.) log5625-log525=2log5h
6.) logx=5log4
9-10: Using Logarithms to Solve Exponential Equations
Learning Target: I will be able to determine values of logarithms; use logarithms to solve exponential equations; apply properties of logarithms; create and apply exponential growth and decay models.
EX: Recall that the formula for interest compounded continuously is A=Pert. At what rate of interest, compounded continuously, do you have to invest your money so that it will triple in 20 years?
EX: The amount of radioactivity from a nuclear explosion is estimated to be modeled by A=A0e-2t, where t is the number of days since the explosion. How long will it take for the radioactivity to reach 11000 of its original intensity?
EX: Solve 5x=32 by taking:
a.) The common logarithm of each side.
b.) The natural logarithm of each side.
c.) Graphically.
Change of Base Theorem:
logba=
EX: Approximate log424 to three decimal places.
EX: Carl plans to invest $500 at 8.25% interest, compounded continuously. How long will it take for his money to triple?
EX: A certain strain of bacteria grows from 40 to 326 in 120 minutes. Find the growth rate of the bacteria.
EX: A $40,000 car depreciates at a constant rate of 12% per year. In how many years will the car be worth $12,000?
*This example is compounded ______, not ______.
EX: Lizzy inherited $1000 from her grandmother. She plans to give her niece $3000 when she graduates from high school. If she puts the inheritance in the bank and earns 10% interest compounded continuously, when will she have $3000 for the gift?
EX: Solve log6x=2
EX: The Allen Electric Company has a piece of machinery valued at $60,000. It depreciates at 20% per year. After how many years will the value have depreciated to $15,000?
HW Pg.647 2-4, 8-21
Worksheet on Logarithms
Quiz 9.5-9.10 tomorrow