Find the Domain log base 5 of 256/4=y

Problem

(log_5)(256/4)=y

Solution

1. Identify the components of the logarithmic equation. The expression is in the form (log_b)(x)=y where the argument is x=256/4

2. Simplify the argument of the logarithm by performing the division.

256/4=64

3. Rewrite the equation with the simplified argument.

(log_5)(64)=y

4. Determine the domain of the logarithmic function. For any function ƒ(x)=(log_b)(g(x)) the domain is defined by the inequality g(x)>0

5. Evaluate the condition for the domain. Since the argument 64 is a constant and 64>0 the expression is defined for all real numbers if y is treated as the dependent variable. However, if the task asks for the domain of the specific constant expression provided, it is simply the set of all real numbers ℝ because the argument is always positive.

Final Answer

Domain: *(−∞,∞)

Want more problems? Check here!