Solving Exponential And Logarithmic Equations MA1310 Week 2

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MA1310:Week2Solving Exponential and Logarithmic EquationsPage1MA1310: Week 2Solving Exponential and LogarithmicEquationsThis lab requires you to:Use like bases to solve exponential equations.Use logarithms to solve exponential equations.Use the definition of a logarithm to solvelogarithmic 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 thislab:1.Solve the exponential equation by expressing each side as a power of the same baseand then equating exponents.6x= 2166^(x)=216Create equivalent expressions in the equation that all have equal bases.6^(x)=6^(3)Since the bases are thesame, then two expressions are only equal if the exponentsare also equal.(x)=3Remove the parentheses around the expression x.x=3

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MA1310:Week2Solving Exponential and Logarithmic EquationsPage22.Solve the exponential equation. Express the solution in terms of natural logarithms.Then use a calculator to obtain a decimal approximation for the solution.ex= 22.8e^(x)=22.8Take the natural logarithm of both sides of the equation to remove the variable fromthe exponent.ln(e^(x))=ln(22.8)The left-hand side of the equation is equal to the exponent of the logarithmargument 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=3.133.Solve the following logarithmic equation. Be sure to reject any value ofxthat is notin the domain of the original logarithmic expression. Give the exact answer.log7x= 2log^7(x)=2Let both sides of the equation be the exponent of base 7.7^(log^7(x))=7^(2)
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