3.4 solving exponential and logarithmic equations
TRANSCRIPT
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
Page 221 – 224
18-28 even, 29-37 odd, 45-69 odd, 86-104 even, 131, 137