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Answer :
Sure! Let's look at how to rewrite the exponential equation [tex]\(2^x = 128\)[/tex] as a logarithmic equation.
1. Understand the Components: In an exponential equation like [tex]\(a^b = c\)[/tex], [tex]\(a\)[/tex] is the base, [tex]\(b\)[/tex] is the exponent, and [tex]\(c\)[/tex] is the result of the exponentiation.
2. Rewrite as a Logarithm: To convert this into a logarithm, we need to identify these components:
- The base of the logarithm is the same as the base of the exponent, which is [tex]\(2\)[/tex].
- The argument of the logarithm (the number we are taking the log of) is the result of the exponentiation, which is [tex]\(128\)[/tex].
- The exponent itself, [tex]\(x\)[/tex], becomes the result of the logarithmic expression.
3. Logarithmic Form: So, the equivalent logarithmic equation is:
[tex]\[
\log_2 128 = x
\][/tex]
This expression means that [tex]\(x\)[/tex] is the power to which the base [tex]\(2\)[/tex] must be raised to produce the number [tex]\(128\)[/tex]. Therefore, option [tex]\(\log_2 128 = x\)[/tex] correctly represents the logarithmic form of the equation [tex]\(2^x = 128\)[/tex].
1. Understand the Components: In an exponential equation like [tex]\(a^b = c\)[/tex], [tex]\(a\)[/tex] is the base, [tex]\(b\)[/tex] is the exponent, and [tex]\(c\)[/tex] is the result of the exponentiation.
2. Rewrite as a Logarithm: To convert this into a logarithm, we need to identify these components:
- The base of the logarithm is the same as the base of the exponent, which is [tex]\(2\)[/tex].
- The argument of the logarithm (the number we are taking the log of) is the result of the exponentiation, which is [tex]\(128\)[/tex].
- The exponent itself, [tex]\(x\)[/tex], becomes the result of the logarithmic expression.
3. Logarithmic Form: So, the equivalent logarithmic equation is:
[tex]\[
\log_2 128 = x
\][/tex]
This expression means that [tex]\(x\)[/tex] is the power to which the base [tex]\(2\)[/tex] must be raised to produce the number [tex]\(128\)[/tex]. Therefore, option [tex]\(\log_2 128 = x\)[/tex] correctly represents the logarithmic form of the equation [tex]\(2^x = 128\)[/tex].
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