Expand the Logarithmic Expression log base b of x^7y

Problem

(log_b)(x^7*y)

Solution

1. Identify the product inside the logarithm, which is x^7⋅y

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

(log_b)(x^7*y)=(log_b)(x^7)+(log_b)(y)

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

(log_b)(x^7)=7*(log_b)(x)

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

7*(log_b)(x)+(log_b)(y)

Final Answer

(log_b)(x^7*y)=7*(log_b)(x)+(log_b)(y)

Want more problems? Check here!