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log_(10)1,000,000=

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

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Convert between exponential and logarithmic form: all bases

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Q.

\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 $\log_{10}1,000,000 = 6$ .

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