what is the value of $log_{625}5$?\n-4\n$-\frac{1}{4}$\n$\frac{1}{4}$\n4

Answer:

C. $\frac{1}{4}$

Explanation:

Step1: Recall the logarithm definition

If $y = \log_{a}x$, then $x=a^{y}$. Let $y=\log_{625}5$, so $5 = 625^{y}$.

Step2: Rewrite 625 as a power of 5

Since $625=5^{4}$, the equation $5 = 625^{y}$ becomes $5=(5^{4})^{y}$.

Step3: Apply power - of - a - power rule

By the rule $(a^{m})^{n}=a^{mn}$, we have $(5^{4})^{y}=5^{4y}$. So $5 = 5^{4y}$.

Step4: Equate the exponents

If $a^{m}=a^{n}$, then $m = n$. For $5 = 5^{4y}$, we get $1 = 4y$.

Step5: Solve for y

Dividing both sides of $1 = 4y$ by 4 gives $y=\frac{1}{4}$.