Question

(a)$5^3=125,$so width="96" height="27" role="math">log=.

(b)${\log }_{5}25=2$ so${\boxed{}}^{\boxed{}}=\boxed{}$.

Short answer

a.$5^3=125,\text{\hspace{0.17em}\hspace{0.17em}so\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{\log }_{5}125=3$

b.${\log }_{5}25=2,\text{\hspace{0.17em}\hspace{0.17em}so\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{5}^2=25$

Step-by-step solution

Part a. Step 1. Given.

The given expression is $5^3=125$.

Part a. Step 2. To determine.

We have to express it using log.

Part a. Step 3. Calculation.

We’ll use the definition $a^b=c\Rightarrow {\log }_{a}c=b$.

We compare$a^b=c$ with $5^3=125$.

So, $a=5,b=3,c=125$.

So, the equivalent expression is:

$$\begin{gathered} {\log }_{a}c=b \\ {\log }_{5}125=3 \end{gathered}$$

Hence, $5^3=125,\text{\hspace{0.17em}\hspace{0.17em}so\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{\log }_{5}125=3$.

Part b. Step 1. Given.

The given expression is ${\log }_{5}25=2$.

Part b. Step 2. To determine.

We have to express it using log.

Part b. Step 3. Calculation.

We’ll use the definition ${\log }_{a}c=b\Rightarrow a^b=c$.

We compare${\log }_{a}c=b$ with ${\log }_{5}25=2$.

So, $a=5,b=2,c=25$.

So, the equivalent expression is:

$$\begin{gathered} a^b=c \\ {5}^2=25 \end{gathered}$$

Hence, ${\log }_{5}25=2,\text{\hspace{0.17em}\hspace{0.17em}so\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{5}^2=25$.