Simplify/Condense 1/2* log base 6 of 9+ log base 6 of 5

Problem

1/2*(log_6)(9)+(log_6)(5)

Solution

1. Apply the Power Property of logarithms, which states n*(log_b)(x)=(log_b)(xn) to the first term.

1/2*(log_6)(9)=(log_6)(9(1/2))

2. Simplify the exponent by calculating the square root of 9.

(log_6)(9(1/2))=(log_6)(3)

3. Apply the Product Property of logarithms, which states (log_b)(x)+(log_b)(y)=(log_b)(x*y) to combine the terms.

(log_6)(3)+(log_6)(5)=(log_6)(3⋅5)

4. Multiply the arguments to find the final condensed form.

(log_6)(3⋅5)=(log_6)(15)

Final Answer

1/2*(log_6)(9)+(log_6)(5)=(log_6)(15)

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