Question

Evaluating Logarithms Evaluate the expression.

(a)${\log }_{2}2$ (b) ${\log }_{5}1$ (c)${\log }_6{6}^5$

Short answer

1. The required value is 1.
2. The required value is 0.
3. The required value is 5.

Step-by-step solution

Part a. Step 1. Given.

The given exponential form is ${\log }_{2}2$.

Part a. Step 2. To determine.

We have to evaluate the given expression.

Part a. Step 3. Calculation.

We’ll use the formula: ${\log }_a\left(a^b\right)=b$.

We will write in form to find a and b. Then we’ll get the answer.

Given	${\log }_{2}2$form	a	b	Answer
${\log }_{2}2$	${\log }_2\left(2^1\right)$	2	1	1

Hence, ${\log }_{2}2$has value $=1$.

Part b. Step 1. Given.

The given exponential form is ${\log }_{5}1$.

Part b. Step 2. To determine.

We have to evaluate the given expression.

Part b. Step 3. Calculation.

We’ll use the formula: ${\log }_a\left(a^b\right)=b$.

We will write ${\log }_{5}1$in form${\log }_a\left(a^b\right)$ to find a and b. Then we’ll get the answer.

Given	${\log }_a\left(a^b\right)$form	a	b	Answer
${\log }_{5}1$	${\log }_5\left(5^0\right)$	5	0	0

Hence, ${\log }_{5}1$has value $=0$.

Part c. Step 1. Given.

The given exponential form is ${\log }_6{6}^5$.

Part c. Step 2. To determine.

We have to evaluate the given expression.

Part c. Step 3. Calculation.

We’ll use the formula: ${\log }_a\left(a^b\right)=b$.

We will write ${\log }_6{6}^5$in form${\log }_a\left(a^b\right)$ to find a and b. Then we’ll get the answer.

Given	${\log }_a\left(a^b\right)$form	a	b	Answer
${\log }_6{6}^5$	${\log }_6\left(6^5\right)$	6	5	5

Hence, ${\log }_6{6}^5$has value $=5$.