3.4 Solving Exponential and Logarithmic Equations

In General

1) If you start with an exponential equation you rewrite in log form

or

you take the log of both sides

2) If you start with a log equation you rewrite in exponential form.

In both cases, use your properties to solve

Solving Exponential Equations

72xe

2) 5 36x

3 2 42x

4) 24 3 2xe

5) 2 3 24 7x x

2 52 3 4 11x

7) 2 2 0x xe e

8)

52

x xe e

Solving Logarithmic Equations

ln 2x

10) 3 3log 5 1 log 7x x

11) 5 2ln 4x

12)

52log 3 4x

13) ln 2 ln 2 1 2lnx x x

14) log 5 3 log 1 2x x

Doubling an Investment

You have deposited $500 in an account that pays 6.75% interest, compounded continuously. How long will it take you money to double?

rtA Pe

Average Salary for Public School Teachers

For selected years from 1985 to 2004, the average salary y (in thousands of dollars) for public school teachers for the year t can be modeled by the equation

y=-1.562 + 14.584 ln t, 5≤t≤24.

where t =5 represents 1985. During which year did the average salary for public school teachers reach $44,000?

Homework

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18-28 even, 29-37 odd, 45-69 odd, 86-104 even, 131, 137