The domain of the function f defined by f(x) = ₓ 10 is

Correct Answer is : x>0 excluding x=1x > 0 { excluding } x = 1x>0 excluding x=1

Correct Answer is : x>0 excluding x=1x > 0 { excluding } x = 1x>0 excluding x=1

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UPSC NDA I 2019 Mathematics Solved Paper

Question : 74 of 120

Marks: +1, -0

f

f(x) = \log_{x} 10

Solution:

Concept:

The logarithm

\log_{x}10

is defined only when the base

x

is positive and not equal to

1

Explanation:

Write

f(x) = \log_{x}10

using the change‑of‑base formula:

f(x) = \dfrac{\log 10}{\log x}

For

f(x)

to be a real number, the denominator

\log x

must be defined and non‑zero.

\log x

is defined only when

x > 0

\log x = 0

when

x = 1

, so

x

cannot be

1

Thus the function exists for all

x > 0

except

x = 1

Answer:

Option D:

x > 0

excluding

x = 1

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