$\"\"$

\

The running time to analyze algorithm $\"\"$ , where $\"\"$ is number of steps.

\

a.

\

Find running time to analyze algorithm of $\"\"$ steps.

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

Change of base formula is $\"\"$ .

\

Apply change of base formula to logarithm expression $\"\"$ .

\

$\"\"$

\

Running time to analyze algorithm of $\"\"$ steps is $\"\"$ seconds.

\

$\"\"$

\

b.

\

Find number of steps in an algorithm with a running time of $\"\"$ seconds.

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

The definition of logarithm logarithm is : $\"\"$ if and only if $\"\"$ .

\

$\"\"$

\

Number of steps in an algorithm is $\"\"$ .

\

$\"\"$

\

a. Running time to analyze algorithm of $\"\"$ steps is $\"\"$ seconds.

\

b. Number of steps in an algorithm is $\"\"$ .