Expand the Logarithmic Expression log base 5 of cube root of x^2+1

Problem

(log_5)(√(3,x2+1))

Solution

1. Rewrite the radical expression using a fractional exponent.

(log_5)(x2+1)

2. Apply the power rule for logarithms, which states (log_b)(Mp)=p*(log_b)(M)

1/3*(log_5)(x2+1)

3. Identify if further expansion is possible. Since the argument x2+1 is a sum and not a product or quotient, the expression cannot be expanded further.

Final Answer

(log_5)(√(3,x2+1))=1/3*(log_5)(x2+1)

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