Solving Logarithmic Functions Math 3 Standard MM3A2

Steps:Example 1: 1) Isolate the Logarithm ◦ Condense the logarithm if you have to 2) Translate the equation from logarithmic form to exponential form ◦

Steps:Example 1: 3) Solve for x ◦ In this case, simplify the power first ◦ Then, multiply by 3 ◦ Take the square root of each side  When you take a square root, remember to use +

Steps:Example 1: 4) Check for extraneous solutions ◦ Plug your solution(s) in to the original equation ◦ Use your calculator to check it ◦ This one gives a non-real answer The only real solution is x=17.321

Steps:Example 2: 1) Isolate the Logarithm ◦ Condense the logarithm if you have to 2) Translate the equation from logarithmic form to exponential form ◦

Steps:Example 2: 3) Solve for x ◦ In this case, simplify the power first ◦ Then, take the sixth root of each side  When you take a even root, remember to use +

Steps:Example 2: 4) Check for extraneous solutions ◦ Plug your solution(s) in to the original equation ◦ Use your calculator to check it ◦ This one gives a non-real answer The only real solution is x=6.813

Steps:Example 3: 1) Isolate the Logarithm ◦ Condense the logarithm if you have to 2) Translate the equation from logarithmic form to exponential form ◦

Steps:Example 3: 3) Solve for x ◦ In this case, simplify the power first ◦ Then, divide by 5 ◦ Then, take the third root of each side

Steps:Example 3: 4) Check for extraneous solutions ◦ Plug your solution(s) in to the original equation ◦ Use your calculator to check it The solution is x=12.599

Steps:Example 4: 1) Isolate the Logarithm ◦ You do not have to condense this one 2) Translate the equation from logarithmic form to exponential form ◦

Steps:Example 4: 3) Solve for x ◦ In this case, simplify the power first ◦ Then, add 13

Steps:Example 4: 4) Check for extraneous solutions ◦ Plug your solution(s) in to the original equation ◦ Use your calculator to check it The solution is x=10013

Steps:Example 5: 1) Isolate the Logarithm ◦ Condense the logarithm if you have to 2) Translate the equation from logarithmic form to exponential form ◦

Steps:Example 5: 3) Solve for x ◦ In this case, simplify the power first ◦ Then, multiply by 7

Steps:Example 5: 4) Check for extraneous solutions ◦ Plug your solution(s) in to the original equation ◦ Use your calculator to check it The solution is x=

Steps:Example 6: 1) Isolate the Logarithm ◦ You do not have to condense this logarithm 2) Translate the equation from logarithmic form to exponential form ◦

Steps:Example 6: 3) Solve for x ◦ In this case, simplify the power first ◦ Then, subtract 8 ◦ Then, divide by 3

Steps:Example 6: 4) Check for extraneous solutions ◦ Plug your solution(s) in to the original equation ◦ Use your calculator to check it The solution is x=