Which of the following uses the properties of logarithms to correctly evaluate log1023

Question

?(1 point)
Responses

log1023=23
logarithm 10 superscript 23 baseline equals 23

log1023=−23
logarithm 10 superscript 23 baseline equals negative 23

log1023=10−23
logarithm 10 superscript 23 baseline equals 10 superscript negative 23 baseline

log1023=1023

Answer 1

To evaluate \( \log_{10} 23 \), we need to understand the properties of logarithms.

The correct evaluation is not provided among the options you've given. Specifically, \( \log_{10} 23 \) is asking for the exponent to which the base (10) must be raised to obtain 23.

Mathematically:

\[ 10^x = 23 \]

So, \( x = \log_{10} 23 \) is not equal to any of the options listed (23, -23, \( 10^{-23} \), or \( 10^{23} \)). The logarithm does not simplify in those ways.

To reiterate, the value \( \log_{10} 23 \) is approximately 1.3617, which does not correspond to any of the choices given.

If you are looking for an evaluation or further simplification, none of these options are correct for the logarithm of 23 with a base of 10.