Evaluate log base 8 of 0.25

Problem

(log_8)(0.25)

Solution

1. Convert the decimal value 0.25 into a fraction.

(log_8)(0.25)=(log_8)(1/4)

2. Express both the base and the argument as powers of 2

8=2

1/4=2(−2)

3. Substitute these powers into the logarithm.

(log_2)(2(−2))

4. Apply the change of base formula or the property (log_bn)(am)=m/n*(log_b)(a)

(−2)/3*(log_2)(2)

5. Simplify the expression using the identity (log_b)(b)=1

(−2)/3⋅1=−2/3

Final Answer

(log_8)(0.25)=−2/3

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