Question

Let $x=(0.15{)}^{20}$. Find the characteristic in the logarithm of $x$ to the base $10$.

• A. $17$
• B. $21$
• C. $-21$
• D. $-17$

Answer 1

Answer: (D)

$-17$

Given $x=(0.15{)}^{20}$

By applying $\log$ on both sides , we get ${\log }_{10}x=20{\log }_{10}\left(0.15\right)=-16.478$

$\Rightarrow {\log }_{10}x=-17+0.5218$

The integral part of ${\log }_{10}x$ is called characteristic

Therefore the characteristic of given number is $-17$

So option $D$ is correct