find an approximation to the nearest ten-thousandth
log 8900 over log 110
An answer to the nearest ten-thousandth is NOT an approximation.
Here is what I would call an approximation ....
log 8900 is close to log 10000 which is 4
log 110 is close to log 100 which is 2
so an approximation answer would be 4/2 or 2
calculator answer is 1.93 (not bad)
To find an approximation to the nearest ten-thousandth of log 8900 over log 110, we can follow these steps:
Step 1: Use a calculator or a computer program with a logarithm function.
Step 2: Calculate the logarithm of 8900 with base 10. This can be denoted as log10(8900). The result is approximately 3.949390006860066, where the digits shown are rounded to the last decimal place.
Step 3: Calculate the logarithm of 110 with base 10. This can be denoted as log10(110). The result is approximately 2.041392685158225, where the digits shown are rounded to the last decimal place.
Step 4: Divide the result from step 2 (3.949390006860066) by the result from step 3 (2.041392685158225).
3.949390006860066 / 2.041392685158225 ≈ 1.934148906
Hence, an approximation to the nearest ten-thousandth of log 8900 over log 110 is approximately 1.9341.