Identify base, number, exponent: Identify the base (b), the number (x), and the exponent (y) that the logarithm is equal to. In the logarithmic equation log_(10)1,000, the base b is 10 and the number x is 1,000. We need to find the exponent y such that 10^y = 1,000.Recognize power of 10: Recognize that 1,000 is a power of 10. Specifically, 1,000 is 10^3 because 10 * 10 * 10 = 1,000.Write exponential form: Write the exponential form of the logarithmic equation. Since we know that 10^3 = 1,000, the logarithmic equation log_(10)1,000 is equal to 3.Confirm equivalence: Confirm that the exponential form matches the original logarithmic equation. The logarithmic equation log_(10)1,000 = 3 is equivalent to the exponential equation 10^3 = 1,000.

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Algebra 2

Convert between exponential and logarithmic form: all bases

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\log _{10} 1,000=

Identify base, number, exponent: Identify the base $b$ , the number $x$ , and the exponent $y$ that the logarithm is equal to. $\newline$ In the logarithmic equation $\log_{10}1000$ , the base $b$ is $10$ and the number $x$ is $1000$ . We need to find the exponent $y$ such that $10^y = 1000$ .
Recognize power of $10$ : Recognize that $1,000$ is a power of $10$ . Specifically, $1,000$ is $10^3$ because $10 \times 10 \times 10 = 1,000$ .
Write exponential form: Write the exponential form of the logarithmic equation. Since we know that $10^3 = 1,000$ , the logarithmic equation $\log_{10}1,000$ is equal to $3$ .
Confirm equivalence: Confirm that the exponential form matches the original logarithmic equation. The logarithmic equation $\log_{10}1000 = 3$ is equivalent to the exponential equation $10^3 = 1,000$ .