Identify b, x, and y: Identify b, x, and y. Compare log_(10)10,000 with log_(b)x = y. b = 10 x = 10,000 y = unknownUnderstand the definition of a logarithm: Understand the definition of a logarithm. The logarithm log_(b)x = y means that b raised to the power y equals x. So, log_(10)x = y means 10^y = x.Apply the definition to the given logarithm: Apply the definition to the given logarithm. Since log_(10)10,000 is given, we want to find y such that 10^y = 10,000. We know that 10^4 = 10,000. Therefore, y = 4.Write the exponential form of the logarithmic equation: Write the exponential form of the logarithmic equation. Since we found that y = 4, the exponential form is 10^4 = 10,000.

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

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Algebra 2

Convert between exponential and logarithmic form: all bases

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\log _{10} 10,000=

Identify $b$ , $x$ , and $y$ : Identify $b$ , $x$ , and $y$ . $\newline$ Compare $\log_{(10)} 10,000$ with $\log_{(b)}x = y$ . $\newline$ $b = 10$ $\newline$ $x = 10,000$ $\newline$ $x$ $0$
Understand the definition of a logarithm: Understand the definition of a logarithm. $\newline$ The logarithm $\log_{b}x = y$ means that $b$ raised to the power $y$ equals $x$ . $\newline$ So, $\log_{10}x = y$ means $10^y = x$ .
Apply the definition to the given logarithm: Apply the definition to the given logarithm. $\newline$ Since $\log_{10} 10,000$ is given, we want to find $y$ such that $10^y = 10,000$ . $\newline$ We know that $10^4 = 10,000$ . $\newline$ Therefore, $y = 4$ .
Write the exponential form of the logarithmic equation: Write the exponential form of the logarithmic equation. $\newline$ Since we found that $y = 4$ , the exponential form is $10^4 = 10,000$ .