Was given a study guide with no answers Very unhelpful as I

Was given a study guide with no answers.... Very unhelpful as I don\'t have a means of checking my answers.

6. Solve each of the following equations for x a. eln(2x)=4 bloga 5)2 c, logs(25x2)-6 d, log,(1) = 7- Let j(r) = 4 ln(r) What is the average rate of change of)(r) with respect to r as the value of r changes from 9 to 5.

Solution

a) e^ln 2x = 4

taking natural log on both sides

ln 2x = ln 4

or 2x = 4

x = 2

b) log ₈ ( x- 5) = 2

changing it to exponnetial form

x - 5 = 8^2

x - 5 = 64

x = 69

c) log ₅ ( 25x^2 ) = 6

changing to exponential form

25x^2 = 5^6

x^2 = 5^6 / 25

x^2 = 5^4

x = +- 25

d) log ₃ ( 1) = x

applying change of base formula on left side

log 1 / log 3 = x

x = 0