To convert the logarithmic equation [tex]\( 5 = \log_5 M \)[/tex] into its equivalent exponential form, we use the property of logarithms that [tex]\( \log_b(a) = c \)[/tex] is equivalent to [tex]\( b^c = a \)[/tex].
Here, the base [tex]\( b \)[/tex] is 5, the exponent [tex]\( c \)[/tex] is 5, and the result [tex]\( a \)[/tex] is [tex]\( M \)[/tex].
So, the equation [tex]\( 5 = \log_5 M \)[/tex] can be rewritten in exponential form as:
[tex]\[ 5^5 = M \][/tex]
Therefore, the equivalent exponential form of the equation is:
[tex]\[ 5^5 = M \][/tex]