Let for a fixed real number

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Let

f(x)=a^{x}

for a fixed real number

a>1

. Answer the following. (i) Define an increasing real-valued function on

\mathbb R

. (ii) Prove that

f(x)

is an increasing function on

\mathbb R

. (iii) Using the conclusion of part (ii), arrange the numbers

3^{0.18},\,3^{0.20},\,3^{0.25}

in descending order and justify your answer.