Solve for x 10x 391 ex 57 Solution1 ex 1 1e e1 Therefor

Solution

1. e^{x + 1} = 1/e = e^-1 . Therefore, x + 1 = -1 so that x = - 1 -1 = -2

There is some ambiguity about the R. H. S. If e^{x + 1} = 1/8 , then , on taking natural logarithms of both the sides, we have (x + 1)ln e = ln (1/8) or, x + 1 = - 2.079 ( approx) so that x = - 3.079 ( ln e = 1)

2. 10^x = 3.91. On taking logarithms ( to the base 10) of both the sides, we have x log 10 = log 3.91 or, x = 0.592 ( apprximately, as log 10 = 1)

3. e^x  = 5.7. Then, on taking natural logarithms of both the sides, we have x ln e = ln 5.7 or, x = 1.74 ( approximately as ln e = 1)