An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

Apply the quotient rule of logarithms: lo g 5 ​ ( y 5 ​ ) = lo g 5 ​ ( 5 ) − lo g 5 ​ ( y ) .
Simplify lo g 5 ​ ( 5 ) to 1 .
The final expanded expression is 1 − lo g 5 ​ ( y ) .
Therefore, the answer is 1 − lo g 5 ​ ( y ) ​ .

Explanation

Understanding the Problem We are given the logarithmic expression lo g 5 ​ ( y 5 ​ ) and asked to expand it using properties of logarithms.

Applying the Quotient Rule We will use the quotient rule of logarithms, which states that the logarithm of a quotient is the difference of the logarithms: lo g b ​ ( N M ​ ) = lo g b ​ ( M ) − lo g b ​ ( N ) .

Rewriting the Expression Applying this rule to our expression, we get: lo g 5 ​ ( y 5 ​ ) = lo g 5 ​ ( 5 ) − lo g 5 ​ ( y ) .

Simplifying the Logarithm Now we simplify lo g 5 ​ ( 5 ) . Recall that lo g b ​ ( b ) = 1 for any base b . Therefore, lo g 5 ​ ( 5 ) = 1 .

Final Expanded Expression Substituting this back into our expression, we have: 1 − lo g 5 ​ ( y ) .
This is the fully expanded form of the given logarithmic expression.


Examples
Logarithms are used in many real-world applications, such as measuring the intensity of earthquakes (the Richter scale), the loudness of sounds (decibels), and the acidity of a solution (pH scale). Understanding how to expand and simplify logarithmic expressions can help in analyzing and interpreting data in these fields. For example, if you know the ratio of two sound intensities, you can use the properties of logarithms to find the difference in their decibel levels. Suppose the intensity of a concert is 1000 times greater than the intensity of normal conversation. Using logarithms, we can easily calculate the difference in decibel levels: lo g 10 ​ ( 1000 ) = 3 , which means the concert is 30 decibels louder (since each unit on the logarithmic scale represents 10 decibels).

Answered by GinnyAnswer | 2025-07-03

Approximately 2.81 × 1 0 21 electrons flow through the electric device delivering 15.0 A of current for 30 seco n d s . This is calculated using the total charge and the charge of a single electron.
;

Answered by Anonymous | 2025-07-04