Evaluate 3 log of 1/(10^2)

Problem

3*(log_)(1/10)

Solution

1. Rewrite the fraction using a negative exponent to simplify the argument of the logarithm.

1/10=10(−2)

2. Substitute the simplified expression back into the original problem.

3*(log_)(10(−2))

3. Apply the power rule of logarithms, which states (log_)(ab)=b*(log_)(a)

3⋅(−2)*(log_)(10)

4. Evaluate the common logarithm (log_)(10) which is equal to 1 because 10=10

3⋅(−2)⋅1

5. Multiply the remaining constants to find the final value.

−6

Final Answer

3*(log_)(1/10)=−6

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