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Answer :
To rewrite the exponential equation [tex]\(2^x = 128\)[/tex] as a logarithmic equation, let's follow these steps:
1. Understand the Connection Between Exponential and Logarithmic Forms:
- In general, the exponential form [tex]\(b^y = a\)[/tex] can be rewritten in logarithmic form as [tex]\(\log_b a = y\)[/tex], where:
- [tex]\(b\)[/tex] is the base,
- [tex]\(y\)[/tex] is the exponent,
- [tex]\(a\)[/tex] is the result of the exponentiation.
2. Identify Parts from the Original Equation:
- In the equation [tex]\(2^x = 128\)[/tex], we can identify:
- The base [tex]\(b = 2\)[/tex],
- The exponent [tex]\(x\)[/tex] (which we are solving for),
- The result of the exponentiation [tex]\(a = 128\)[/tex].
3. Rewrite in Logarithmic Form:
- Using the structure [tex]\(\log_b a = y\)[/tex], we replace [tex]\(b\)[/tex] with 2, [tex]\(a\)[/tex] with 128, and [tex]\(y\)[/tex] with [tex]\(x\)[/tex].
- This gives us the logarithmic equation: [tex]\(\log_2 128 = x\)[/tex].
Therefore, the correct logarithmic form of the equation [tex]\(2^x = 128\)[/tex] is [tex]\(\log_2 128 = x\)[/tex].
1. Understand the Connection Between Exponential and Logarithmic Forms:
- In general, the exponential form [tex]\(b^y = a\)[/tex] can be rewritten in logarithmic form as [tex]\(\log_b a = y\)[/tex], where:
- [tex]\(b\)[/tex] is the base,
- [tex]\(y\)[/tex] is the exponent,
- [tex]\(a\)[/tex] is the result of the exponentiation.
2. Identify Parts from the Original Equation:
- In the equation [tex]\(2^x = 128\)[/tex], we can identify:
- The base [tex]\(b = 2\)[/tex],
- The exponent [tex]\(x\)[/tex] (which we are solving for),
- The result of the exponentiation [tex]\(a = 128\)[/tex].
3. Rewrite in Logarithmic Form:
- Using the structure [tex]\(\log_b a = y\)[/tex], we replace [tex]\(b\)[/tex] with 2, [tex]\(a\)[/tex] with 128, and [tex]\(y\)[/tex] with [tex]\(x\)[/tex].
- This gives us the logarithmic equation: [tex]\(\log_2 128 = x\)[/tex].
Therefore, the correct logarithmic form of the equation [tex]\(2^x = 128\)[/tex] is [tex]\(\log_2 128 = x\)[/tex].
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