Subjects algebra

Logarithm Evaluation 892104

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1. The problem is to evaluate $\log 0.00012$.\n\n2. Recall that logarithms convert multiplication and division into addition and subtraction, and that $\log a^b = b \log a$.\n\n3. Express $0.00012$ in scientific notation: $0.00012 = 1.2 \times 10^{-4}$.\n\n4. Use the logarithm property: $$\log(1.2 \times 10^{-4}) = \log 1.2 + \log 10^{-4}.$$\n\n5. Calculate each term: $\log 1.2$ is approximately $0.07918$, and $\log 10^{-4} = -4$ because $\log 10^n = n$.\n\n6. Add the results: $$\log 0.00012 = 0.07918 - 4 = -3.92082.$$\n\n7. Therefore, the value of $\log 0.00012$ is approximately $-3.92082$.