Question

The logarithm of 0.1 to the base 10 is equal to
A. 3
B. -2
C. -1
D. 4

Answer 1

Hint: The conversion of logarithmic function to exponential functions is given by,
\[lo{{g}_{b}}(x)=y\Leftrightarrow {{b}^{y}}=x,b>0,b\ne 1\], where the base given by b is always positive, because for negative base logarithmic functions are not defined.

Complete Step-by-Step solution:
To solve such questions, we first of all need to know the basic knowledge of converting logarithmic functions into exponential functions so that it is easily accessible and solvable for us. Theory of logarithmic functions converted to exponential functions and vice versa is given as,
\[lo{{g}_{b}}(x)=y\Leftrightarrow {{b}^{y}}=x,b>0,b\ne 1\]…….(i)
Note that the base b is always positive.
Given in the question we have to find the value of the logarithm of 0.1 to the base 10.
Comparing from what is given by equation(i) we have in our case, the base b = 10, x = 0.1 and we have to find the value of y.
Converting the following logarithmic function into exponential function we get,
\[{{10}^{y}}=0.1\]
Solving this above obtained expression by proper substitution we get,
\[{{10}^{y}}={{(10)}^{-1}}\]
Comparing both the sides of the above obtained expression we get,
The value of y = -1.
Therefore, we obtain that the value of logarithm of 0.1 to the base 10 is -1.
Hence, we obtain the correct answer as -1 which is option (c).

Note: The possibility of error in this question can be getting the base of log as negative which would be wrong because for the negative values logarithmic functions are not defined, therefore always observe that the base of log should be positive and not negative.