Question

Logarithmic Form Express the equation in logarithmic form.

(a)$4^x=70$ (b)$3^5=w$

Short answer

1. Logarithmic form of $4^x=70$is ${\log }_4\left(70\right)=x$.
2. Logarithmic form of $3^5=w$is ${\log }_3\left(w\right)=5$.

Step-by-step solution

Part a. Step 1. Given.

The given exponential form is $4^x=70$.

Part a. Step 2. To determine.

We have to find the exponential form.

Part a. Step 3. Calculation.

We’ll use the formula:$a^b=c$ is equivalent to ${\log }_{a}c=b$.

Comparing we find the values of a, b, c. Then plug them in the exponential form.

Exponential form ($a^b=c$)	a	b	c	Logarithmic form (${\log }_{a}c=b$)
$4^x=70$	4	x	70	${\log }_4\left(70\right)=x$

Hence, logarithmic form of $4^x=70$is ${\log }_4\left(70\right)=x$.

Part b. Step 1. Given.

The given exponential form is $3^5=w$.

Part b. Step 2. To determine.

We have to find the exponential form.

Part b. Step 3. Calculation.

We’ll use the formula:$a^b=c$ is equivalent to ${\log }_{a}c=b$.

Comparing we find the values of a, b, c. Then plug them in the exponential form.

Exponential form ($a^b=c$)	a	b	c	Logarithmic form (${\log }_{a}c=b$)
$3^5=w$	3	5	w	${\log }_3\left(w\right)=5$

Hence, logarithmic form of $3^5=w$is ${\log }_3\left(w\right)=5$.