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Answer :
To solve the question "Which of the following is equivalent to [tex]\( \log_5(125) \)[/tex]?" we need to find the value of [tex]\( x \)[/tex] such that:
[tex]\[ 5^x = 125 \][/tex]
Let's break it down step-by-step:
1. Recognize what the logarithm means: The expression [tex]\(\log_5(125)\)[/tex] is asking us to find the power [tex]\( x \)[/tex] to which we must raise 5 to get 125. Mathematically, it's saying [tex]\( 5^x = 125 \)[/tex].
2. Express 125 as a power of 5: To solve [tex]\( 5^x = 125 \)[/tex], we need to express 125 using base 5. We notice that:
[tex]\[
5 \times 5 \times 5 = 125
\][/tex]
Therefore:
[tex]\[
5^3 = 125
\][/tex]
3. Deduce the logarithm value: Since [tex]\( 5^3 = 125 \)[/tex], we can conclude that:
[tex]\[
x = 3
\][/tex]
Hence, the logarithm [tex]\(\log_5(125)\)[/tex] is equivalent to 3. So, the answer to the question is 3.
[tex]\[ 5^x = 125 \][/tex]
Let's break it down step-by-step:
1. Recognize what the logarithm means: The expression [tex]\(\log_5(125)\)[/tex] is asking us to find the power [tex]\( x \)[/tex] to which we must raise 5 to get 125. Mathematically, it's saying [tex]\( 5^x = 125 \)[/tex].
2. Express 125 as a power of 5: To solve [tex]\( 5^x = 125 \)[/tex], we need to express 125 using base 5. We notice that:
[tex]\[
5 \times 5 \times 5 = 125
\][/tex]
Therefore:
[tex]\[
5^3 = 125
\][/tex]
3. Deduce the logarithm value: Since [tex]\( 5^3 = 125 \)[/tex], we can conclude that:
[tex]\[
x = 3
\][/tex]
Hence, the logarithm [tex]\(\log_5(125)\)[/tex] is equivalent to 3. So, the answer to the question is 3.
Thank you for reading the article Which of the following is equivalent to tex log 5 125 tex A 3 B 5 C 625 D 25. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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