If 10 7=a, then 10 (1/70 ) is equal to

ABC26GN2077 · Logarithms

Subject: General Aptitude · Chapter: Logarithms · Exam: 2003 · Marks: · Difficulty:

If $\log _{10} 7=a$, then $\log _{10}\left(\frac{1}{70}\right)$ is equal to

(a)$-(1+a)$

(b)$(1+a)^{-1}$

(c)$\frac{a}{10}$

(d)$\frac{1}{10 a}$

Answer

Answer (as printed): A

Explanation

$\log _{10}\left(\frac{1}{70}\right)=\log _{10} 1-\log _{10} 70=-\log _{10}$ $$(7 \times 10)=-\left(\log _{10} 7+\log _{10} 10\right)=-(a+1) .$$

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