An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
The problem asks which property justifies simplifying lo g b ( b x + y ) to x + y .
The key property is lo g b ( b c ) = c .
Applying this property with c = x + y gives lo g b ( b x + y ) = x + y .
Therefore, the answer is lo g b ( b c ) = c .
Explanation
Understanding the Problem We are asked to identify the property that justifies the simplification of the expression lo g b ( b x + y ) to x + y .
Listing Possible Properties The possible properties are: b x ⋅ b y = b x + y , substitution, lo g b ( b c ) = c , and the commutative property.
Identifying the Correct Property The property lo g b ( b c ) = c is the property that justifies the simplification.
Applying the Property In this case, c = x + y , so lo g b ( b x + y ) = x + y .
Conclusion Therefore, the answer is lo g b ( b c ) = c .
Examples
Logarithms are used to solve exponential equations, which are common in science and engineering. For example, the growth of bacteria, the decay of radioactive materials, and the compound interest formula all involve exponential equations. The property lo g b ( b c ) = c is useful in simplifying these equations.
