Evaluate the given expressions (to two decimal places).
(a) ) log((23.0)
(b) ) log_(2) \(128\)
(c) ) log_(9) \(1\)
To evaluate the given expressions, we will use the properties of logarithms.
(a) Evaluate log(23.0):
The notation "log(23.0)" refers to the logarithm with base 10 of 23.0. To evaluate this expression, you can use a scientific calculator or logarithm tables.
If you're using a scientific calculator:
- Enter the value 23.0.
- Press the "log" or "logarithm" button.
- The calculator will display the result.
If you're using logarithm tables:
- Locate the value 23.0 in the logarithm table.
- Take note of the corresponding logarithm value.
(b) Evaluate log base 2 of 128:
The notation "log_(2) 128" refers to the logarithm with base 2 of 128. To evaluate this expression, you can again use a scientific calculator or logarithm tables.
If you're using a scientific calculator:
- Enter the value 128.
- Press the "log" or "logarithm" button.
- Divide the result by the logarithm of 2.
- The calculator will display the final result.
If you're using logarithm tables:
- Locate the value 128 in the logarithm table.
- Take note of the corresponding logarithm value.
- Divide the logarithm value by the logarithm of 2.
(c) Evaluate log base 9 of 1:
The notation "log_(9) 1" refers to the logarithm with base 9 of 1. In general, the logarithm of 1 to any base is always 0.
Therefore, log base 9 of 1 is equal to 0 in this case.
Remember to round your final answers to two decimal places if necessary.