Question

If log10 7 = a, then log10(1/70) is equal to: op 1: -(1 + a)

Answer 1

check the solution
ans is correct

Answer 2

Answer:

$\log_{10}(\frac{1}{70})=-(1+a)$

Step-by-step explanation:

Given : If  $\log_{10}7=a$

To find : The value of $\log_{10}(\frac{1}{70})$

Solution :

Applying logarithmic properties to distribute the expression,

$\log_{10}(\frac{1}{70})$

Using $\log (\frac{a}{b})=\log a-\log b$

$\log_{10}(\frac{1}{70})=\log_{10} 1-\log_{10} 70$

We know, $\log_{10} 1=0$

$\log_{10}(\frac{1}{70})=0-\log_{10} 70$

$\log_{10}(\frac{1}{70})=\log_{10} (10\times 7)$

Using $\log(ab)=\log a+\log b$

$\log_{10}(\frac{1}{70})=-(\log_{10} 10+\log_{10} 7)$

We know, $\log_{10} 10=1$ and $\log_{10}7=a$

$\log_{10}(\frac{1}{70})=-(1+a)$

Therefore, Option 1 is correct.