Answer :
To solve the equation
[tex]$$
\log_5 3125 = x,
$$[/tex]
we are looking for the exponent [tex]$x$[/tex] such that
[tex]$$
5^x = 3125.
$$[/tex]
Notice that [tex]$3125$[/tex] is a power of [tex]$5$[/tex]. In fact,
[tex]$$
3125 = 5^5.
$$[/tex]
Since the base and the exponent match, we have
[tex]$$
5^x = 5^5.
$$[/tex]
By comparing the exponents, we obtain
[tex]$$
x = 5.
$$[/tex]
Thus, the solution is [tex]$\{5\}$[/tex], which corresponds to option A.
[tex]$$
\log_5 3125 = x,
$$[/tex]
we are looking for the exponent [tex]$x$[/tex] such that
[tex]$$
5^x = 3125.
$$[/tex]
Notice that [tex]$3125$[/tex] is a power of [tex]$5$[/tex]. In fact,
[tex]$$
3125 = 5^5.
$$[/tex]
Since the base and the exponent match, we have
[tex]$$
5^x = 5^5.
$$[/tex]
By comparing the exponents, we obtain
[tex]$$
x = 5.
$$[/tex]
Thus, the solution is [tex]$\{5\}$[/tex], which corresponds to option A.
