Solve the following exponential equation. Express the solution in terms of natur
ID: 2911963 • Letter: S
Question
Solve the following exponential equation. Express the solution in terms of natural logarithms or comme decimal approximation for the solution. 53x + 5 = 7x-4 The solution set expressed in terms of logarithms is - (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for an 5 In (5) +4 In (7) 31n(5)-In(7) logarithm and log for common logarithm.) Now use a calculator to obtain a decimal approximation for the solution. The solution set is -5.49 (Use a comma to separate answers as needed. Round to two decimal places as needed.)Explanation / Answer
5^(3x+5) = 7^(x-4)
taking ln on both sides
( 3x + 5 ) ln 5 = ( x- 4 ) ln 7
3x ln 5 + 5 ln 5 = x ln 7 - 4 ln 7
5 ln 5 + 4 ln 7 = x ln 7 - 3x ln 5
x = ( 5 ln 5 + 4 ln 7 ) / ( ln 7 - 3 ln 5 )
solution set is {-5.49 }