Question

convert to the logarithmic equation that has the same meaning. 10^{6}=1,000,000 the equation is (use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Recall the relationship between exponential and logarithmic forms

The exponential form \(a^b = c\) can be converted to the logarithmic form \(\log_a c=b\). In the given equation \(10^6 = 1000000\), \(a = 10\), \(b = 6\), and \(c=1000000\).

Step2: Apply the conversion formula

Using the formula \(\log_a c=b\), we substitute \(a = 10\), \(b = 6\), and \(c = 1000000\). So the logarithmic form is \(\log_{10}1000000=6\). Since \(\log_{10}x\) is often written as \(\lg x\), it can also be written as \(\lg1000000 = 6\).

Answer:

\(\log_{10}1000000 = 6\) (or \(\lg1000000=6\))