Question
Convert to a logarithmic equation. \( 10^{6}=1,000,000 \) (Use integers or fractions for any numbers in the equation.)
Ask by Guerrero Carlson. in the United States
Nov 17,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(\log_{10}(1,000,000) = 6\)
Solution
To convert the exponential equation \( 10^{6} = 1,000,000 \) into a logarithmic equation, we can use the definition of a logarithm. The general form is:
\[
b^y = x \quad \text{is equivalent to} \quad \log_b(x) = y
\]
In this case, we have:
- \( b = 10 \)
- \( y = 6 \)
- \( x = 1,000,000 \)
Thus, the logarithmic equation is:
\[
\log_{10}(1,000,000) = 6
\]
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Simplify this solution Extra Insights
The equation \( 10^{6} = 1,000,000 \) can be converted to a logarithmic equation by expressing it in the form of \( \log_b(a) = c \). Here, the base \( b \) is 10, the value \( a \) is 1,000,000, and the exponent \( c \) is 6. Therefore, the logarithmic equation is: \[ \log_{10}(1,000,000) = 6. \] And there you have it! Logarithms turning the exponential party into a more laid-back gathering. If you're ever confused about logs, remember that they’re like the reverse of exponents! Instead of asking "10 raised to what power equals 1,000,000?”, we now ask, "What power do I raise 10 to get 1,000,000?" And pow! Logarithms come to the rescue.
