Determine if True log base 4 of 0.0625=-2

Problem

(log_4)(0.0625)=−2

Solution

1. Convert the decimal value 0.0625 into a fraction to make it easier to compare with the base.

0.0625=625/10000

2. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, 625

625/10000=1/16

3. Rewrite the logarithmic equation in its equivalent exponential form, by=x where the base b=4 the exponent y=−2 and the value x=1/16

4(−2)=1/16

4. Apply the negative exponent rule, a(−n)=1/(an) to evaluate the left side of the equation.

4(−2)=1/4

5. Calculate the power of the denominator.

1/4=1/16

6. Compare the results to determine the truth value. Since 1/16=1/16 the original statement is true.

Final Answer

(log_4)(0.0625)=−2* is True

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