Using the techniques of Section 11.5, solve the following natural logarithmic functions for x: (a) 7 ln

Using the techniques of Section 11.5, solve the following natural logarithmic functions for x:

Transcribed Image Text:

(a) 7 ln x 2.6 = 10 - Solving algebraically for Inx, 7 ln x = 12.6, In x = 1.8 Setting both sides of the equation as exponents of e to eliminate the natural log, From (11.2), elnx = 1.8 e x = 1.8 Using a calculator, as explained in Section 1.7.12, (b) In(x 1.51) = 1.2 x=6.04965 6.05 Simplifying with the laws of logs, then solving for Inx, 3 ln(x 1.51) 1.2 In(x 1.51) 0.4 - Setting both sides of the equation as exponents of e, From (11.2), eln(x-1.51)=0.4 x 1.51 1.49 - x = 3 (c) Inx+2.24 = 2.14 Simplifying and solving, In(x + 2.24) = 2.14 In(x+2.24) 4.28