Answered

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How would you write:
[tex]\[ 6^x = 25 \][/tex]
as a logarithm?

A. [tex]\[ \log_6 25 = x \][/tex]
B. [tex]\[ \log_x 25 = 6 \][/tex]
C. [tex]\[ \log 25 = x \][/tex]
D. [tex]\[ \log_{25} 6 = x \][/tex]

Sagot :

GinnyAnswer
To write the exponential equation [tex]\(6^x = 25\)[/tex] as a logarithm, we need to understand the relationship between exponents and logarithms. For any positive numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] (where [tex]\(a \neq 1\)[/tex]):

[tex]\[a^b = c\][/tex]

can be rewritten using logarithms as:

[tex]\[\log_a(c) = b\][/tex]

Given the equation:

[tex]\[6^x = 25\][/tex]

we can apply this property. Here, [tex]\(a = 6\)[/tex], [tex]\(b = x\)[/tex], and [tex]\(c = 25\)[/tex]. So, to convert this exponential equation into a logarithmic form, we use:

[tex]\[\log_{6}(25) = x\][/tex]

Therefore, the answer is:

A [tex]\(\log_6(25) = x\)[/tex]
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