Evaluate ( log of 16)/( log of 4)

Problem

(log_)(16)/(log_)(4)

Solution

1. Identify the expression as a ratio of logarithms, which can be simplified using the change of base formula or by expressing the numbers as powers of the same base.

2. Rewrite the number 16 as a power of 4 to simplify the numerator.

16=4

3. Substitute this power into the logarithmic expression.

(log_)(4)/(log_)(4)

4. Apply the power rule for logarithms, which states (log_)(bn)=n*(log_)(b) to the numerator.

2*(log_)(4)

5. Simplify the fraction by canceling the common term (log_)(4) from the numerator and the denominator.

(2*(log_)(4))/(log_)(4)=2

Final Answer

(log_)(16)/(log_)(4)=2

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