ABC26GN2097 · Logarithms

Subject: General Aptitude · Chapter: Logarithms · Exam: · Marks: · Difficulty:

If $\log 2=0.30103$, then the number of digits in $5^{20}$ is
(a)14
(b)16
(c)18
(d)25
Answer
Answer (as printed): A
Explanation
$$\begin{aligned} \log 5^{20} & =20 \log 5=20 \times\left[\log \left(\frac{10}{2}\right)\right]=20(\log 10-\log 2) \\ & =20(1-0.3010)=20 \times 0.6990=13.9800 . \end{aligned}$$ ∴ Characteristic $=13$. Hence, the number of digits in $5^{20}$ is 14.

Explanation as extracted from the printed page; notation may be imperfect.

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