To find the logarithm [tex]\(\log (1,000,000)\)[/tex], we need to determine the power to which 10 must be raised to result in 1,000,000.
1. Understand the problem: The notation [tex]\(\log (1,000,000)\)[/tex] typically refers to the common logarithm, which is the logarithm with base 10. So, we need to solve:
[tex]\[
\log_{10} (1,000,000)
\][/tex]
2. Rewrite the number using exponents: Begin by expressing 1,000,000 as a power of 10:
[tex]\[
1,000,000 = 10^6
\][/tex]
3. Apply the logarithm properties: One of the basic properties of logarithms is:
[tex]\[
\log_{b} (b^k) = k
\][/tex]
Since our base [tex]\( b \)[/tex] is 10 and [tex]\( k \)[/tex] is 6, this simplifies to:
[tex]\[
\log_{10} (10^6) = 6
\][/tex]
4. Conclusion: Therefore,
[tex]\[
\log_{10} (1,000,000) = 6
\][/tex]
So, the value of [tex]\(\log (1,000,000)\)[/tex] is [tex]\( 6.0 \)[/tex].
