Question

Solve the logarithmic equation.

log₃ (y +15) = log₃(y-5)+ log₃5
What is the equivalent algebraic equation that must be solved?

A. 3(y+15)=3(y-5)+3(5)
B. y + 15=5(y-5)
C. y +15=(y-5)+5
D. y + 15 = y-5/5

Answer 1

The equivalent algebraic equation to solve the logarithmic equation log₃ (y +15) = log₃(y-5)+ log₃(5) is B. y + 15 = 5(y-5).

Step-by-step explanation:

To solve the given logarithmic equation, we can use the properties of logarithms. The equation log₃ (y +15) = log₃(y-5)+ log₃(5) can be simplified using the property that the log of a product is the sum of the logs. Therefore, we can combine the right side to get log₃ ((y-5)×5). This gives us log₃ (y +15) = log₃ (5y-25). Since the logs have the same base and are equal, their arguments must also be equal given that logarithmic functions are one-to-one. This simplifies to the algebraic equation y + 15 = 5(y-5), which is our answer B.