Part 4: Logarithms
Section 1: Solving regular equations with logarithms
Example: 10^(2x) = 15
On Paper: Put log in front of both sides of the equation. (log(10^(2x) = log(15)) Then use the operation of logarithms and put the exponent in front of log (2x•log(10) = log(15)). From here you can divide each side to get the x by itself (2x•log(10)/2log(10) = log(15)/ 2log(10)). This should leave x by itself (x=log(15)/ 2log(10)). Now it's ready to be put into the calculator.
On Calculator: Put in your equation into the calculator by using the log key. (log(15)/2log(10)). Press the enter key and your answer should come up on the screen.
On Paper: Put log in front of both sides of the equation. (log(10^(2x) = log(15)) Then use the operation of logarithms and put the exponent in front of log (2x•log(10) = log(15)). From here you can divide each side to get the x by itself (2x•log(10)/2log(10) = log(15)/ 2log(10)). This should leave x by itself (x=log(15)/ 2log(10)). Now it's ready to be put into the calculator.
On Calculator: Put in your equation into the calculator by using the log key. (log(15)/2log(10)). Press the enter key and your answer should come up on the screen.
Section: 2 Solving irregular equations with natural logarithms
Example: e^(2x) = 10
On Paper: This is similar to solving regular equations with logarithms except the natural log (ln) key is used in place of the log key. Begin by writing down your equation. Get the natural log (ln) of each side. (ln(e^(2x)) = ln(10)) Use the operation of logarithms and put the exponent in front. (2x•ln(e) = ln(10) The rule of the number e and natural logarithms is that if you have ln(e) it is equal to 1, so change ln(e) to 1, which is basically the same as just taking it out completely. (2x = ln(10) Then divide to get x by itself. (2x/2 = ln(10)/2) (x = ln(10)/2) The equation is ready to be entered into the calculator.
On Calculator: Enter your equation into the calculator using the natural logarithm key (ln). Press enter and your answer should appear on the screen.
On Paper: This is similar to solving regular equations with logarithms except the natural log (ln) key is used in place of the log key. Begin by writing down your equation. Get the natural log (ln) of each side. (ln(e^(2x)) = ln(10)) Use the operation of logarithms and put the exponent in front. (2x•ln(e) = ln(10) The rule of the number e and natural logarithms is that if you have ln(e) it is equal to 1, so change ln(e) to 1, which is basically the same as just taking it out completely. (2x = ln(10) Then divide to get x by itself. (2x/2 = ln(10)/2) (x = ln(10)/2) The equation is ready to be entered into the calculator.
On Calculator: Enter your equation into the calculator using the natural logarithm key (ln). Press enter and your answer should appear on the screen.
Section 3: Change of base formula
Example: Log base 4 (10)
When calculating logarithms on this particular calculator, it is assumed that the base is 10. This cannot be changed with a button, but it can be with a formula. If you want log base 4 (10), start out by pressing the log key and then typing 10. Then press the division key. After that, press the log key again and then type in 4. This should give you log base 4 (10).
When calculating logarithms on this particular calculator, it is assumed that the base is 10. This cannot be changed with a button, but it can be with a formula. If you want log base 4 (10), start out by pressing the log key and then typing 10. Then press the division key. After that, press the log key again and then type in 4. This should give you log base 4 (10).
Section 4: graphing logarithms
To graph logarithms, first enter your equations into the calculator by pressing the Y= button and typing it into the Y1 space. Press enter. Then press graph and your equation should come up on the graph.
Section 5: Logarithmic regression
When working with logarithmic regression, the stat menu will be utilized on your calculator. Press the stat button, and then choose option 1 which is Edit. Press enter and plug in your stats in the table. These should be numbers that start off slow and far apart (1, 20, 30) and then grow faster and closer together (30, 35, 38). After plugging your numbers in, press second, stat plot and press option 1 which should say plot off. Flash over on and press enter. This turns your stat plotting on so you can see your graph correctly. Then press graph and you should see your plots on the graph. To find your equation to make your line of best fit, press the stat button and go over to CALC and down to option 9, LnReg. Press enter and that should show up on your screen. Press enter again and the equation show come up on the screen. To actually get the line of best fit, press Y=. To copy and paste the equation into this so you don't have to write it down, press VARS, go down to statistics, press enter, go over to EQ and press option 1, RegEQ. This will paste your equation into the Y=. Press enter. Now press the graph button and your line of best fit should show up on your graph.
Section 6: Scientific Notation
When you are doing a problem on the calculator, and you see something like 1.254678E13, this just means that your answer is 1.254678 multiplied by 10^13, or the decimal moves to the right 13 times. If it shows up with a negative number, that just means your number is really small, and the decimal would be moved over to the left 13 times, making it a really small number.