Evaluate log base 8 of 0.125

Problem

(log_8)(0.125)

Solution

1. Convert the decimal 0.125 into a fraction.

0.125=125/1000

2. Simplify the fraction by dividing both the numerator and the denominator by 125

125/1000=1/8

3. Rewrite the expression using the simplified fraction.

(log_8)(0.125)=(log_8)(1/8)

4. Express the fraction as a power of the base 8 using the rule 1/x=x(−1)

1/8=8(−1)

5. Apply the logarithm property (log_b)(bx)=x to evaluate the expression.

(log_8)(8(−1))=−1

Final Answer

(log_8)(0.125)=−1

Want more problems? Check here!