Question

Given $\log 6$ and $\log 8$, then the only logarithm that cannot be obtained without using the table is

• A. $\log 64$
• B. $\log 21$
• C. $\log$ $\frac{8}{3}$
• D. $\log 9$

Answer 1

The correct option is B $\log 21$

We have,

$\log 6$ and $\log 8$

We know that

$\log 6=\log 3+\log 2$

$\log 8=\log 4+\log 2$

Therefore, by using $\log 6$ and $\log 8$, we can calculate

$\log 64=\log 8^2=2\log 8$

$\log 9=\log 3^2=2\log 3$

$\log \frac{8}{3}=\log 8-\log 3$

But we can not find $\log 21$ using $\log 6$ and $\log 8$.

Hence, this is the answer.