To solve for [tex]\(\log_{66} 32\)[/tex], we need to determine the power to which the base 66 must be raised to get 32.
In mathematical terms, we are looking for the value [tex]\(x\)[/tex] in the equation:
[tex]\[ 66^x = 32 \][/tex]
Using logarithms, particularly change of base formula, we can express this as:
[tex]\[ \log_{66} 32 = \frac{\log 32}{\log 66} \][/tex]
By evaluating the logs, we determine the required power.
Given the computations:
[tex]\[ \log_{66} 32 \approx 0.8272127695952917 \][/tex]
This tells us that [tex]\(\log_{66} 32\)[/tex] is approximately [tex]\(0.8272\)[/tex] to four decimal places. Thus:
[tex]\[ \log_{66} 32 \approx 0.8272 \][/tex]
This is the detailed solution for finding the logarithm of 32 with base 66.
