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

Answer: (B)

$\log 21$

Let $\log 6=x$

$\Rightarrow \log 2+\log 3=x$ ....... $\left(i\right)$

Let $\log 8=y$

$\Rightarrow 3\log 2=y$

$\Rightarrow \log 2=\frac{y}{3}$ ...... $\left(ii\right)$

$\therefore x=\log 3+\frac{y}{3}$ ...... From $\left(i\right)$ and $\left(ii\right)$

$\Rightarrow \log 3=x-\frac{y}{3}$

A.

$\log 64=\log 2^6=6\log 2=6\frac{y}{3}$

B.

$\log 21=\log 3+\log 7$

Thus, $\log 21$ cannot be found from given values as we need the value of $\log 7$.

C.

$\log \frac{8}{3}=\log 8-\log 3=3\log 2-\log 3$

D.

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

Hence, only $\log 21$ can't be obtained from given data.