Chapter C, Problem 1E

In Exercise 1-6, express each equation in logarithmic form.

$2^6=64$

To determine

To express:

The equation in logarithmic form, $2^6=64$.

Answer to Problem 1E

Solution:

The equation in logarithmic form is ${\log }_{2}64=6$.

Explanation of Solution

Given:

The equation is,

$2^6=64$

Approach:

Definition of logarithms,

Logarithm of $x$ to the base $b$, $b>0$, $b\ne 1$

$y={\log }_{b}x$;if and only if $x=b^y$ when $\left(x>0\right)$.

Calculation:

Consider the expression.

$2^6=64$

Apply the above rule of logarithm.

$\begin{array}{rll}6& =& {\log }_{2}64\\ {\log }_{2}64& =& 6\end{array}$

Therefore, the equation in logarithmic form is ${\log }_{2}64=6$.

Conclusion:

Hence, the equation in logarithmic form is ${\log }_{2}64=6$.