Question

a. (x)-In(ex) b. f(x) = lnx In
Use properties of logarithms to rewrite each function.

Answer 1

f(x) = ln (e^2 x) we know that ln(a, b) = ln(a) = ln (b) f(x) = ln(e^2) + ln(x) we have property that ln(a^b) = b middot ln(a) so ln(e^2) = 2 middot ln(e) = 2 middot 1 [Because ln_e (e) = 1] = 2 Since natural logarithm of e is 1 Therefore f(x) = 2 + ln (x) f(x) = ln (x/e^2) We have property that ln(a/b) = ln(a) - ln(b) f(x) = ln(x) - ln(e^2) from above ln(e^2) = 2 middot ln(e) = 2.1 = 2 f(x) = ln(x) - 2