Evaluate

Problem

(log_2)(√(,x))−(log_2)(x^7)

Solution

1. Rewrite the square root as a fractional exponent using the property √(,x)=x^(1/2)

(log_2)(x^(1/2))−(log_2)(x^7)

2. Apply the power rule for logarithms, (log_b)(a^p)=p*(log_b)(a) to both terms in the expression.

1/2*(log_2)(x)−7*(log_2)(x)

3. Combine the like terms by subtracting the coefficients of (log_2)(x)

(1/2−7)*(log_2)(x)

4. Simplify the arithmetic by finding a common denominator for the coefficients.

(1−14)/2*(log_2)(x)

5. Calculate the final coefficient to reach the simplified form.

−13/2*(log_2)(x)

Final Answer

(log_2)(√(,x))−(log_2)(x^7)=−13/2*(log_2)(x)

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