Use the ALEKS calculator to evaluate each expression.
Round your answers to the nearest thousandth.
Do not round any intermediate computations.

Ask by Simmons Wang. in the Philippines

Dec 07,2024

Question

Use the ALEKS calculator to evaluate each expression.
Round your answers to the nearest thousandth.
Do not round any intermediate computations.

Ask by Simmons Wang. in the Philippines

Dec 07,2024

UpStudy AI · Accepted Answer

I'm unable to directly calculate the logarithmic expressions using the ALEKS calculator. However, I can guide you on how to calculate them manually.

1. To calculate $$ \log \frac{37}{8} $$:
   - Use the property of logarithms: $$ \log \frac{a}{b} = \log a - \log b $$
   - Calculate $$ \log 37 - \log 8 $$
   - Use a calculator to find the logarithms of 37 and 8
   - Subtract the logarithm of 8 from the logarithm of 37

2. To calculate $$ \log \sqrt{6} $$:
   - Use the property of logarithms: $$ \log \sqrt{a} = \frac{1}{2} \log a $$
   - Calculate $$ \frac{1}{2} \log 6 $$
   - Use a calculator to find the logarithm of 6
   - Divide the logarithm of 6 by 2

Let's calculate these expressions step by step.
Calculate the value by following steps:
- step0: Calculate:
  $$\log_{10}{\left(37\right)}-\log_{10}{\left(8\right)}$$
- step1: Use the logarithm product rule:
  $$\log_{10}{\left(\frac{37}{8}\right)}$$
- step2: Rewrite the expression:
  $$\log_{10}{\left(37\right)}-3\log_{10}{\left(2\right)}$$
The value of $$ \log \frac{37}{8} $$ is approximately 0.665.

Next, let's calculate $$ \log \sqrt{6} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{2}\log_{10}{\left(6\right)}$$
- step1: Multiply:
  $$\frac{\log_{10}{\left(6\right)}}{2}$$
The value of $$ \log \sqrt{6} $$ is approximately 0.389.

Therefore, the rounded values to the nearest thousandth are:
- $$ \log \frac{37}{8} \approx 0.665 $$
- $$ \log \sqrt{6} \approx 0.389 $$
$$ \log \frac{37}{8} \approx 0.665 $$ $$ \log \sqrt{6} \approx 0.389 $$

Use the ALEKS calculator to evaluate each expression.
Round your answers to the nearest thousandth.
Do not round any intermediate computations.

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Use the ALEKS calculator to evaluate each expression. Round your answers to the nearest thousandth. Do not round any intermediate computations.

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Use the ALEKS calculator to evaluate each expression.
Round your answers to the nearest thousandth.
Do not round any intermediate computations.