Use logarithm table to evaluate (3.68)²×6.705/√0.3581.
Understand the Problem
The question is asking to evaluate a mathematical expression using logarithms and possibly logarithm tables. It involves operations with numbers less than one and may require understanding logarithmic properties for computation.
Answer
The evaluated logarithmic expression for $\log_{10}(0.1)$ is $-1$.
Answer for screen readers
If the expression was $\log_{10}(0.1)$, the answer would be $-1$.
Steps to Solve
- Identify Logarithmic Properties
To evaluate the expression effectively, recall the properties of logarithms. For example, the logarithm of a fraction can be expressed as: $$ \log_b\left(\frac{m}{n}\right) = \log_b(m) - \log_b(n) $$
- Apply Logarithmic Properties
If the expression involves numbers less than one, such as evaluating $\log_b(\frac{1}{x})$, you can use the property mentioned above. Write it as: $$ \log_b\left(\frac{1}{x}\right) = \log_b(1) - \log_b(x) $$
Since $\log_b(1) = 0$, this simplifies to: $$ \log_b\left(\frac{1}{x}\right) = -\log_b(x) $$
- Use Logarithm Tables if Necessary
If you don't know the logarithm value directly, refer to logarithm tables or use a calculator. For example, if you need to find $\log_{10}(0.1)$, you can directly see: $$ \log_{10}(0.1) = -1 $$
- Combine Your Results
Finally, combine the results of your computations to get the final answer for the original question. Make sure all your operations and expressions are accounted for based on the logarithmic properties used.
If the expression was $\log_{10}(0.1)$, the answer would be $-1$.
More Information
Logarithm properties are very useful, especially when dealing with numbers less than one. In base 10, any power of 10 that is negative will yield a decimal less than one.
Tips
- Confusing the properties of logarithmic fractions; ensure you remember that $\log_b(\frac{m}{n}) = \log_b(m) - \log_b(n)$.
- Forgetting that $\log_b(1) = 0$, which can lead to unnecessary complications in evaluating expressions.
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