Simplify/Condense

Problem

2*(log_2)(25)−2*(log_2)(5)+(log_2)(3)

Solution

1. Apply the power property of logarithms, n*(log_b)(x)=(log_b)(xn) to the first two terms.

(log_2)(25)−(log_2)(5)+(log_2)(3)

2. Evaluate the exponents inside the logarithms.

(log_2)(625)−(log_2)(25)+(log_2)(3)

3. Apply the quotient property of logarithms, (log_b)(x)−(log_b)(y)=(log_b)(x/y) to the first two terms.

(log_2)(625/25)+(log_2)(3)

4. Simplify the fraction inside the logarithm.

(log_2)(25)+(log_2)(3)

5. Apply the product property of logarithms, (log_b)(x)+(log_b)(y)=(log_b)(x*y)

(log_2)(25⋅3)

6. Multiply the values to find the final condensed form.

(log_2)(75)

Final Answer

2*(log_2)(25)−2*(log_2)(5)+(log_2)(3)=(log_2)(75)

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