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Logarithms and exponents solve equations

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Logarithms and exponents solve equations

1. 1. Logarithms Solving Logarithmic Equations Solving Exponential Equations using Logarithms
2. 2. Solve by changing the form <ul><li>Logarithms  exponents </li></ul><ul><li>If it is written as a logarithm and it cannot be solved, change it to exponential form. </li></ul><ul><li>EX: </li></ul>
3. 3. Change-of-Base Formula <ul><li>Change of Base Formula is used so you can calculate any base in the calculator using base 10 or base e – be sure to end parentheses on top ( ) </li></ul><ul><li>EX: </li></ul>
4. 4. Solve by changing the form <ul><li>Exponents  logarithms </li></ul><ul><li>If it is written as an exponent and it cannot be solved (because bases are not =), change it to logarithmic form. [use change of base formula] </li></ul><ul><li>EX:   </li></ul>
5. 5. Solve by making same base <ul><li>Logs </li></ul><ul><li>If logarithms have the same base, then the numbers behind them must also be equal. Take off the logs, set them equal, and solve for the variable. </li></ul><ul><li>EX: </li></ul>
6. 6. Solve by making same base <ul><li>Logs using properties </li></ul><ul><li>In order to solve a logarithmic equation, you may have to condense into a single logarithm first, using the properties of logarithms </li></ul><ul><li>EX: </li></ul>
7. 7. Solve by making same base <ul><li>Logs using change of base </li></ul><ul><li>If a logarithm cannot be solved by changing it to exponent form, use the change-of-base formula to make base 10 or e , then put it in the calculator to solve. </li></ul><ul><li>EX: </li></ul>
8. 8. Solve by making same base <ul><li>Exponents </li></ul><ul><li>If exponents have the same base, then the exponents must also be equal. Take off the bases, set the exponents equal, and solve for the variable. If bases are not equal, but can be changed to be equal, then do that first.  </li></ul><ul><li>EX: </li></ul>
9. 9. Solve by making same base <ul><li>Exponents using properties </li></ul><ul><li>You may need to combine exponential expressions to solve </li></ul><ul><li>EX: </li></ul>
10. 10. Compound Interest Formulas <ul><li>compounded n times per year: </li></ul><ul><li>A= amount \$ in account at any point in time (accrued) </li></ul><ul><li>P= amount \$ initially deposited in account (principal at start) </li></ul><ul><li>r= % interest rate on the account (written in decimal form) </li></ul><ul><li>t= amount of time the \$ is in the account (typically in years) </li></ul><ul><li>n = the number of times per year the interest is calculated </li></ul>
11. 11. Compound Interest Formulas <ul><li>compounded &quot;continuously: </li></ul><ul><li>A= amount \$ in account at any point in time (accrued) </li></ul><ul><li>P= amount \$ initially deposited in account (principal at start) </li></ul><ul><li>r= % interest rate on the account (written in decimal form) </li></ul><ul><li>t= amount of time the \$ is in the account (typically in years) </li></ul>
12. 12. Example <ul><li>You invest \$6000 into an account paying 3.75% annual interest compounded bimonthly(twice a month), and you want to have \$10,000 saved for your first year of college.  How long will it take for your investment to grow that large?  Round your answer to the nearest whole number. </li></ul>
13. 13. Example <ul><li>You invest \$6000 into an account paying 3.75% annual interest compounded bimonthly (every other month), and you want to have \$10,000 saved for your first year of college. You have a choice to invest your money into an account paying 3.5% annual interest, compounded continuously. Should you choose this compounded continuously account over the other one?  Explain your reasoning. </li></ul>