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Answer :
To rewrite the equation [tex]\( 2^x = 128 \)[/tex] as a logarithmic equation, we use the definition of logarithms. In general, the logarithmic form of the equation [tex]\(a^b = c\)[/tex] is [tex]\(\log_a (c) = b\)[/tex].
For the given equation [tex]\(2^x = 128\)[/tex]:
1. The base [tex]\(a\)[/tex] is 2.
2. The exponent [tex]\(b\)[/tex] is [tex]\(x\)[/tex].
3. The value [tex]\(c\)[/tex] is 128.
Using the definition of logarithms, we rewrite [tex]\(2^x = 128\)[/tex] as:
[tex]\[\log_2 (128) = x\][/tex]
Thus, the correct logarithmic form of the equation [tex]\(2^x = 128\)[/tex] is:
[tex]\[\log_2 128 = x\][/tex]
For the given equation [tex]\(2^x = 128\)[/tex]:
1. The base [tex]\(a\)[/tex] is 2.
2. The exponent [tex]\(b\)[/tex] is [tex]\(x\)[/tex].
3. The value [tex]\(c\)[/tex] is 128.
Using the definition of logarithms, we rewrite [tex]\(2^x = 128\)[/tex] as:
[tex]\[\log_2 (128) = x\][/tex]
Thus, the correct logarithmic form of the equation [tex]\(2^x = 128\)[/tex] is:
[tex]\[\log_2 128 = x\][/tex]
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