Chapter 6.3, Problem 71E

a.

To determine

To evaluate each logarithm expression

Answer to Problem 71E

The value of $x$ is $5^2$ and the value of $b$ is $5^3$

Explanation of Solution

Given information:

Consider the information provided $b$ is given $125$ and $x$ is given $25$

CALCULATION:

As per the given problem,

  $\begin{array}{l}b=125=5\times 5\times 5=5^3\\ x=25=5\times 5=5^2\end{array}$

Therefore, the value of $b$ is $5^3$ and $x$ is $5^2$

b.

To determine

To evaluate each logarithm expression.

Answer to Problem 71E

The value of $x$ is $2^5$ and the value of $b$ is $2^3$

Explanation of Solution

Given information:

Consider the information provided $b$ is given $8$ and $x$ is given $32$

CALCULATION:

As per the given problem,

  $\begin{array}{l}b=8=2\times 2\times 2=2^3\\ x=32=2\times 2\times 2\times 2\times 2=2^5\end{array}$

Therefore, the value of $b$ is $2^3$ and $x$ is $2^5$

c.

To determine

To evaluate each logarithm expression.

Answer to Problem 71E

The value of $x$ is $3^4$ and the value of $b$ is $3^3$

Explanation of Solution

Given information: Consider the information provided $b$ is given $27$ and $x$ is given $81$

CALCULATION:

As per the given problem,

  $\begin{array}{l}b=27=3\times 3\times 3=3^3\\ x=81=3\times 3\times 3\times 3=3^4\end{array}$

Therefore, the value of $b$ is $3^3$ and $x$ is $3^4$

d.

To determine

To evaluate each logarithm expression.

Answer to Problem 71E

The value of $x$ is $2^7$ and the value of $b$ is $2^2$

Explanation of Solution

Given information: Consider the information provided $b$ is given $4$ and $x$ is given $128$

CALCULATION:

As per the given problem,

  $\begin{array}{l}b=4=2\times 2=2^2\\ x=128=2\times 2\times 2\times 2\times 2\times 2\times 2=2^7\end{array}$

Therefore, the value of $b$ is $2^2$ and $x$ is $2^7$