Chapter 10.CR, Problem 1CR

In Exercise 1-3, find the value of $x$.

$x={\log }_{3}81$

To determine

To find:

The value of $x$.

Answer to Problem 1CR

Solution:

The value of $x$ is $4$.

Explanation of Solution

Given:

The equation is $x={\log }_{3}81$.

Approach:

In logarithm, the Exponent-Becomes-Multiplier property is given as,

$\log \left(A^n\right)=n\cdot \log A$

In logarithm, the inverse property is given as,

$\log \left({10}^x\right)=x$

Calculation:

From the data,

$x={\log }_{3}81$

Calculate the value of $x$.

From, Exponent-Becomes-Multiplier property, the above mention equation can be written as,

$\begin{array}{rll}x& =& {\log }_3{\left(3\right)}^4\\ & =& 4\left({\log }_{3}3\right)\end{array}$

From, inverse property the above mention equation can be written as,

$\begin{array}{rll}x& =& 4\left(1\right)\\ & =& 4\end{array}$

Therefore, the value of $x$ is $4$.

Conclusion:

Hence, the value of $x$ is $4$.