
The logarithm of 100 to the base 10 is
(a) 2
(b) 4
(c) 1
(d) 3
Answer
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Hint: Use the fact that the value of the logarithm of ‘x’ to the base ‘y’ is . Write 100 in terms of the exponential power of 10. Further, simplify the expression using the logarithmic formula to get the value of the given expression.
Complete step-by-step answer:
We have to calculate the value of the logarithm of 100 to the base 10.
We know that the value of the logarithm of ‘x’ to the base ‘y’ is .
Substituting in the above expression, the value of the logarithm of 100 to the base 10 is .
We will now write 100 in terms of the exponential power of 10. Thus, we have .
We can rewrite the expression as .
We know the logarithmic formula .
Substituting in the above formula, we have .
Thus, we have .
Hence, the value of the logarithm of 100 to the base 10 is 2, which is option (a).
Note: One must know that the logarithmic functions are the inverse of exponential functions. This means that the logarithm of a number ‘x’ is the exponent to which another fixed number; the base ‘b’ must be raised, to produce that number ‘x’. We observed that base 10 should be raised to power 2 to get 100, i.e., . Logarithm counts the number of occurrences of the same factor in repeated multiplication.
Complete step-by-step answer:
We have to calculate the value of the logarithm of 100 to the base 10.
We know that the value of the logarithm of ‘x’ to the base ‘y’ is
Substituting
We will now write 100 in terms of the exponential power of 10. Thus, we have
We can rewrite the expression
We know the logarithmic formula
Substituting
Thus, we have
Hence, the value of the logarithm of 100 to the base 10 is 2, which is option (a).
Note: One must know that the logarithmic functions are the inverse of exponential functions. This means that the logarithm of a number ‘x’ is the exponent to which another fixed number; the base ‘b’ must be raised, to produce that number ‘x’. We observed that base 10 should be raised to power 2 to get 100, i.e.,
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