Answer:
[tex]\textsf{D.} \quad 5^9=x[/tex]
Step-by-step explanation:
Given logarithmic equation:
[tex]\log_5x-\log_525=7[/tex]
[tex]\textsf{Apply the quotient log law}: \quad log_ax - \log_ay=\log_a \left(\dfrac{x}{y}\right)[/tex]
[tex]\implies \log_5\left(\dfrac{x}{25}\right)=7[/tex]
[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies 5^7=\dfrac{x}{25}[/tex]
Multiply both sides by 25:
[tex]\implies 25 \cdot 5^7=x[/tex]
Rewrite 5 as 5²:
[tex]\implies 5^2 \cdot 5^7=x[/tex]
[tex]\textsf{Apply exponent rule}: \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies 5^{2+7}=x[/tex]
[tex]\implies 5^9=x[/tex]