Question

Complete the steps to evaluate the following expression, given log3a = −0.631.

Answer 1

$\log _{3}(3)=1$ and $\log _{3} \frac{a}{3}=-1.631$

Solution:

Given value $\log _{3} a=-0.631$.

To evaluate the expression $\log _{3} \frac{a}{3}$.

Using logarithmic rule: $\log _{b}\left(\frac{M}{N}\right)=\log _{b}(M)-\log _{b}(N)$

$\log _{3} \frac{a}{3}=\log _{3}(a)-\log _{3}(3)$

We know that $\log _{3} a=-0.631$.

$\log _{3} \frac{a}{3}=-0.631-\log _{3}(3)$

Using another logarithmic rule: $\log _{b} b=1$

$\log _{3} \frac{a}{3}=-0.631-1$

$\log _{3} \frac{a}{3}=-1.631$

Hence $\log _{3}(3)=1$ and $\log _{3} \frac{a}{3}=-1.631$.

Answer 2

$log3^3$ = 1 and the next

$log3\frac{a}{3}$= -1 .631

just did it and got it correct on EDG