Expand the Logarithmic Expression log base 5 of x/2

Problem

(log_5)(x/2)

Solution

1. Identify the logarithmic property for division, which is the Quotient Rule for Logarithms.

2. Apply the formula (log_b)(M/N)=(log_b)(M)−(log_b)(N) to the given expression.

3. Substitute b=5 M=x and N=2 into the rule.

4. Simplify the expression by writing the difference of the two logarithms.

Final Answer

(log_5)(x/2)=(log_5)(x)−(log_5)(2)

Want more problems? Check here!