To solve the given logarithmic equation [tex]\(4 = \log_7 M\)[/tex], we need to convert it to its equivalent exponential form.
The general rule for converting a logarithmic equation [tex]\(\log_b A = C\)[/tex] to its exponential form is:
[tex]\[ A = b^C \][/tex]
Applying this to the given equation:
[tex]\[ \log_7 M = 4 \][/tex]
Here, [tex]\(b\)[/tex] is 7, [tex]\(C\)[/tex] is 4, and [tex]\(A\)[/tex] is [tex]\(M\)[/tex].
So, the equivalent exponential form of the equation is:
[tex]\[ M = 7^4 \][/tex]
Calculating [tex]\(7^4\)[/tex] (7 raised to the power of 4), we get:
[tex]\[ 7^4 = 2401 \][/tex]
Therefore, the value of [tex]\(M\)[/tex] is:
[tex]\[ M = 2401 \][/tex]
