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]
