Chapter 11.CT, Problem 1CT

To determine

To solve:

${\log }_3\sqrt{3}$.

Answer to Problem 1CT

Solution:

The value of ${\log }_3\sqrt{3}=\frac{1}{2}$.

Explanation of Solution

Formulae used:

(1) Exponential form of logarithm is given by

${\log }_{b}r=t$ is equivalent to $b^t=r$.

(2) If $b>0,b\ne 1$ and $m$ and $n$ are real numbers, then $b^n=b^m$ if and only if $n=m$.

Calculation:

Let ${\log }_3\sqrt{3}=x$.

Switch to exponential form.

$3^x=\sqrt{3}$

$3^x=\sqrt{3}$

$3^x=3^{\frac{1}{2}}$

Equate the powers of 3.

$x=\frac{1}{2}$.

Final statement:

The value of ${\log }_3\sqrt{3}=\frac{1}{2}$.