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Answer :
Sure! To rewrite the equation [tex]\(2^x = 128\)[/tex] as a logarithmic equation, we can follow these steps:
1. Understand the relationship:
The expression [tex]\(2^x = 128\)[/tex] is an exponential form where 2 is the base, [tex]\(x\)[/tex] is the exponent, and 128 is the result of raising 2 to that power.
2. Recall the definition of a logarithm:
Generally, a logarithm is expressed as [tex]\(\log_{\text{base}}(\text{number}) = \text{exponent}\)[/tex]. This means that the logarithm of a number with a specific base is the exponent to which the base must be raised to produce that number.
3. Identify the parts for this specific equation:
- Base = 2
- Number = 128
- Exponent = [tex]\(x\)[/tex]
4. Rewrite in logarithmic form:
Using the relationship stated above, we can rewrite the equation by showing that [tex]\(x\)[/tex] is the logarithm of 128 with base 2. Therefore, the equation becomes:
[tex]\[
\log_2 128 = x
\][/tex]
So, the logarithmic form of the equation [tex]\(2^x = 128\)[/tex] is [tex]\(\log_2 128 = x\)[/tex].
1. Understand the relationship:
The expression [tex]\(2^x = 128\)[/tex] is an exponential form where 2 is the base, [tex]\(x\)[/tex] is the exponent, and 128 is the result of raising 2 to that power.
2. Recall the definition of a logarithm:
Generally, a logarithm is expressed as [tex]\(\log_{\text{base}}(\text{number}) = \text{exponent}\)[/tex]. This means that the logarithm of a number with a specific base is the exponent to which the base must be raised to produce that number.
3. Identify the parts for this specific equation:
- Base = 2
- Number = 128
- Exponent = [tex]\(x\)[/tex]
4. Rewrite in logarithmic form:
Using the relationship stated above, we can rewrite the equation by showing that [tex]\(x\)[/tex] is the logarithm of 128 with base 2. Therefore, the equation becomes:
[tex]\[
\log_2 128 = x
\][/tex]
So, the logarithmic form of the equation [tex]\(2^x = 128\)[/tex] is [tex]\(\log_2 128 = x\)[/tex].
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Rewritten by : Barada
