Solving Exponential and Log Equations

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Presentation transcript:

Solving Exponential and Log Equations Solve each equation below for x. Round to 2 decimal places and show work 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Solving Log Equations Practice Part 1 Solve the following log equations for x. Show work! 1. 2. 4. 6. 7. 8. 9. 10. 11. 12. 13.

Notes -Solving Log Equations Part 1 Steps: 1. If there is a number not in a parenthesis that is between the log and the =, add or subtract it to the other side. 2. If there is a number in front of the log, divide by it on both sides. 3. Convert the log equation into an exponential equation. (Remember, log with no base = base 10 and ln is base e) 4. Raise base number in exponential equation to its exponent in the calculator. 5. Set this number = to the expression in the original parenthesis and solve for x. If no parenthesis in the problem, step 5 is not needed. Ex. Ex. Ex.

Notes -Solving Log Equations Part 1 Ex.

Notes -Solving Exponential Equations with logs(or solving e equations) Steps for solving exponentials with logs: 1. If there is a number between the exponent and the =, add or subtract it to the other side. 2. Rewrite problem with a log(same base as in problem) on both sides of =. On left side of =, log and original base used in problem will cancel out. (Remember, log with no base = base 10) 3. Use change of base in calculator to evaluate right side of =. Rewrite left side = to number obtained round to 2 decimal places. 4. Solve for x as normal.(if needed) Ex.

Notes -Solving Exponential Equations with logs(or solving e equations) Steps for solving e equations: 1. If there is a number between the exponent and the =, add or subtract it to the other side. 2. If there is a number in front of the e, divide by it on both sides. 3. Rewrite problem with an “ln” added in the front of each side. On the left side of the =, the ln and the e will cancel out. Bring down the exponent unchanged. 4. Use the calculator to evaluate the right side of the = and round answer to 2 decimal places. Bring this number down. 5. Solve remaining equation for x. (if needed) Ex.

Warmup 12-3 1. Evaluate: 2. Find the inverse: 3. Find the inverse: 4. Condense the following log expression with one log: 5. Condense the following log expression with one log: Expand the following log into multiple logs.

Warmup 12-3 1. Evaluate: 2. Find the inverse: 3. Find the inverse: 4. Condense the following log expression with one log: 5. Condense the following log expression with one log: Expand the following log into multiple logs.