0. Functions

Properties of logarithms Assume logbx = 0.36, logby= 0.56 and logbz = 0.83 . Evaluate the following expressions.

logb (√x) / (³√z)

Determine whether the following statements are true and give an explanation or counterexample.

$2=10^{{\log }_{10}2}$

Determine whether the following statements are true and give an explanation or counterexample.

${\log }_5{4}^6=4{\log }_{5}6$

Determine whether the following statements are true and give an explanation or counterexample.

$2=\ln 2^e$

Simplify the expression e^xln(x²+1).

Explain why or why not. Determine whether the following statements are true and give an explanation or counterexample.

b. ln(x + 1) + ln(x − 1) = ln(x² − 1), for all x.