Expand the Logarithmic Expression log base 5 of 5x^2

Problem

(log_5)(5*x2)

Solution

1. Apply the product rule for logarithms, which states that (log_b)(M*N)=(log_b)(M)+(log_b)(N)

(log_5)(5*x2)=(log_5)(5)+(log_5)(x2)

2. Simplify the first term by evaluating the logarithm of the base, where (log_b)(b)=1

(log_5)(5)=1

3. Apply the power rule for logarithms to the second term, which states that (log_b)(Mp)=p*(log_b)(M)

(log_5)(x2)=2*(log_5)(x)

4. Combine the results to write the fully expanded expression.

1+2*(log_5)(x)

Final Answer

(log_5)(5*x2)=1+2*(log_5)(x)

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