Let be an exponential function with base .

MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

Let

y = 2^{x}

be an exponential function with base

2

. (i) Define the logarithmic function to base

2

and state the restrictions on its base and argument. (ii) Rewrite the statement

2^{5}=32

in logarithmic form. (iii) Show algebraically that

\log_{2}(2^{x}) = x

for every real number

x

, and hence state the domain and range of the function

f(x)=\log_{2}x

. Explain each step of your reasoning.