Problem

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \[ \log \left(\frac{y}{1,000,000}\right) \] \[ \log \left(\frac{y}{1,000,000}\right)= \]

Solution

Step 1 :Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.

Step 2 :The properties of logarithms state that the logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. Therefore, we can rewrite the given expression as: \(\log(y) - \log(1,000,000)\)

Step 3 :The logarithm of 1,000,000 is 6 because 10 to the power of 6 equals 1,000,000. Therefore, the expression simplifies to: \(\log(y) - 6\)

Step 4 :The expanded form of the logarithmic expression is \(\boxed{\log(y) - 6}\)

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Source: https://solvelyapp.com/problems/8126/

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