Hom MT Homework Section 73 Homework 20 Score 0 of 1 pt 7365

Hom MT Homework: Section 7.3 Homework 20 Score: 0 of 1 pt 7.3.65 Solve the following exponential equation. Express irrational solutions in exact form and as a decimal roundec What is the exact answer? Select the correct choice below and, if necessary, fill in the answer box to complet A. The solution set is (Simplify your answer. Type an exact answer.) B. There is no solution. Click to select and enter your answer(s) and then click Check Answer. part

Solution

5^(1-8x) = 4^x

taking log on both sides

(1-8x ) ln 5 = x ln 4

ln 5 - 8x ln 5 = x ln 4

ln 5 = x ( ln 4 + 8 ln 5 )

x = ln 5 / ( ln 4 + 8 ln 5 )

x = 0.112849

rounding to 3 decimal places

x = 0.113