Graph 3 log base 3 of x- log base 3 of y

Problem

3*(log_3)(x)−(log_3)(y)

Solution

1. Identify the expression as a logarithmic expression that can be simplified using the properties of logarithms.

2. Apply the power property of logarithms, which states that n*(log_b)(a)=(log_b)(an) to the first term.

3*(log_3)(x)=(log_3)(x3)

3. Apply the quotient property of logarithms, which states that (log_b)(a)−(log_b)(c)=(log_b)(a/c) to combine the terms.

(log_3)(x3)−(log_3)(y)=(log_3)((x3)/y)

4. Determine the graph by setting the expression equal to a variable, typically z or ƒ(x,y) representing a 3D surface.

z=(log_3)((x3)/y)

5. Identify the domain constraints for the logarithmic function, requiring the argument to be strictly positive.

x>0

y>0

Final Answer

3*(log_3)(x)−(log_3)(y)=(log_3)((x3)/y)

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