Write each equation in its equivalent exponential form Then

Write each equation in its equivalent exponential form. Then solve for x. log_4(2x - 7) = 1 log_7(3x + 1)=2 ln(5x) = 0 The function f(x) = -4.86 In x + 32.5 models the percentage of first-year female college students expressing antifeminist views x years after 1969. Use the function to find the percentage of first-year female college students expressing antifeminist views in 1970. Use the function to find the percentage of first-year female college students expressing antifeminist views in 2014.

Solution

Equivalent Exponential form: loga(x) = b ----> x = a^b

18. log4(2x -7) =1

(2x -7) = 4^1

2x -7 = 4

2x = 11----> x= 11/2 = 5.5

19. log7(3x +1) = 2

3x+1 = 7^2

3x+1 = 49----> 3x = 48

x = 16

20. ln(5x) =0

5x= e^0

5x =1

x = 1/4

21. f(x) = -4.86lnx +32.5

a) perecntage of females exprseeing antifeminist views in 1970

x=1 ; f(1) = -4.86ln(1) +32.5 = 32.5 %

b) in 2014 perecntage of females exprseeing antifeminist views

x= 45yrs

f(45) = -4.86ln(45) +32.5 = 14 %