MA1 3 10 : Week 2 Solving Exponential and Logarithmic Equations Page 1 MA1310: Week 2Solving Exponential and Logarithmic Equations This lab requires you to: • Use like bases to solve exponential equations. • Use logarithms to solve exponential equations. • Use the definition of a logarithm to solve logarithmic equations. • Use the one - to - one property of logarithms to solve logarithmic equations. • Solve applied problems involving exponential and logarithmic equations. • Model exponential growth and decay. Answer the following questions to complete this lab: 1. Solve the exponential equation by expressing each side as a power of the same base and then equating exponents. 6 x = 216 6^(x)=216 Create equivalent expressions in the equation that all have equal bases. 6^(x)=6^(3) Since the bases are the same, then two expressions are only equal if the exponents are also equal. (x)=3 Remove the parentheses around the expression x. x=3 MA1 3 10 : Week 2 Solving Exponential and Logarithmic Equations Page 2 2. Solve the exponential equation. Express the solution in terms of natural logarithms. Then use a calculator to obtain a decimal approximation for the solution. e x = 22.8 e^(x)=22.8 Take the natural logarithm of both sides of the equation to remove the variable from the exponent. ln(e^(x))=ln(22.8) The left - hand side of the equation is equal to the exponent of the logarithm argument because the base of the logarithm equals the base of the argument. x=ln(22.8) The natural logarithm of 22.8 is 3.13. x=(3.13) Remove the parentheses around the expression 3.13. x=3.13 3. Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. Give the exact answer. log 7 x = 2 log^7(x)=2 Let both sides of the equation be the exponent of base 7. 7^(log^7(x))=7^(2)