Identify base, number, and exponent: Identify the base (b), the number (x), and the exponent (y) that the logarithm is trying to find. In the logarithmic equation log_(10)1,000,000, the base b is 10 and the number x is 1,000,000. We are trying to find the exponent y such that 10^y = 1,000,000.Recognize 1,000,000 as a power of 10: Recognize that 1,000,000 is a power of 10. Specifically, 1,000,000 is 10^6 because 10 multiplied by itself 6 times equals 1,000,000. Calculation: 10 * 10 * 10 * 10 * 10 * 10 = 1,000,000.Write exponential form of logarithmic equation: Write the exponential form of the logarithmic equation using the base, the exponent, and the number. Since we know that 10^6 = 1,000,000, we can write the exponential form of the logarithmic equation as log_(10)1,000,000 = 6.

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Algebra 2

Convert between exponential and logarithmic form: all bases

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\log _{10} 1,000,000=

Identify base, number, and exponent: Identify the base ( $b$ ), the number ( $x$ ), and the exponent ( $y$ ) that the logarithm is trying to find. $\newline$ In the logarithmic equation $\log_{10}1,000,000$ , the base $b$ is $10$ and the number $x$ is $1,000,000$ . We are trying to find the exponent $y$ such that $10^y = 1,000,000$ .
Recognize $1,000,000$ as a power of $10$ : Recognize that $1,000,000$ is a power of $10$ . Specifically, $1,000,000$ is $10^6$ because $10$ multiplied by itself $6$ times equals $1,000,000$ . $\newline$ Calculation: $10 \times 10 \times 10 \times 10 \times 10 \times 10 = 1,000,000$ .
Write exponential form of logarithmic equation: Write the exponential form of the logarithmic equation using the base, the exponent, and the number. $\newline$ Since we know that $10^6 = 1,000,000$ , we can write the exponential form of the logarithmic equation as $\log_{10}1,000,000 = 6$ .