Expand the Logarithmic Expression 3 log of c^2+2+ log of 2c^5

Problem

3*(log_)(c2+2)+(log_)(2*c5)

Solution

1. Apply the power property of logarithms to the first term, which states n*(log_)(x)=(log_)(xn)

(log_)((c2+2)3)+(log_)(2*c5)

2. Apply the product property of logarithms, which states (log_)(a)+(log_)(b)=(log_)(a*b)

(log_)((c2+2)3⋅2*c5)

3. Apply the power property to the second term to expand the product inside the logarithm.

(log_)(2*c5*(c2+2)3)

4. Expand the power of the variable inside the second logarithm if needed, though the standard expanded form for logarithmic expressions typically focuses on separating terms using log properties.

3*(log_)(c2+2)+(log_)(2)+5*(log_)(c)

Final Answer

3*(log_)(c2+2)+(log_)(2*c5)=3*(log_)(c2+2)+(log_)(2)+5*(log_)(c)

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