If log₁₀(100) = x, what is the value of x?

To determine the value of ( x ) in the equation ( \log_{10}(100) = x ), we need to understand the definition of a logarithm. The expression ( \log_{10}(100) ) asks the question: "To what power must we raise 10 to obtain 100?"

We can rewrite 100 as a power of 10:

[

100 = 10^2

]

Using this relationship, we can substitute into the logarithmic equation:

[

\log_{10}(100) = \log_{10}(10^2)

]

According to the properties of logarithms, specifically that ( \log_b(a^c) = c \cdot \log_b(a) ), we have:

[

\log_{10}(10^2) = 2 \cdot \log_{10}(10)

]

Since ( \log_{10}(10) = 1 ) (because 10 raised to the power of 1 is 10), we simplify this to:

[

2 \cdot 1 = 2

]

Thus, we find that ( x = 2 ).

This validates the statement that ( \log