what is the value of log10 6.85 to the nearest ten thousandth
To find the value of log base 10 of 6.85 to the nearest ten-thousandth, you can use a calculator or a mathematical software. However, I will guide you through the steps using a calculator:
Step 1: Press the "log" or "log10" button on your calculator, which represents the logarithm function with base 10.
Step 2: Enter the value 6.85.
Step 3: Press the "equals" button (=) to calculate the logarithm.
The result is approximately 0.8356 to the nearest ten-thousandth.
To find the value of log10 6.85 to the nearest ten thousandth, you can use the natural logarithm function and the change of base formula. The change of base formula states that any logarithm can be expressed as the quotient of two logarithms with different bases. In this case, we'll use the natural logarithm, which has a base of e (approximately 2.71828), and convert it to our desired base 10.
Here are the steps to solve it:
Step 1: Calculate loge 6.85. You can use a scientific calculator or a math software to find the natural logarithm of 6.85, which is approximately 1.924.
Step 2: Apply the change of base formula to convert the natural logarithm to base 10. The formula is: logb x = logc x / logc b. In this case, b is 10, and c is e.
log10 6.85 ≈ loge 6.85 / loge 10.
Step 3: Since the natural logarithm of 10 is 2.3026, which is a commonly known value, we substitute it into the formula:
log10 6.85 ≈ 1.924 / 2.3026.
Step 4: Divide 1.924 by 2.3026 to find the value:
log10 6.85 ≈ 0.8362.
Therefore, the value of log10 6.85 to the nearest ten thousandth is approximately 0.8362.