Evaluate \( \log_{\sqrt{2}} 4 + \log_{\frac{1}{2}} 16 - \log_{4} 32 \)
Question 1 Report
Evaluate \( \log_{\sqrt{2}} 4 + \log_{\frac{1}{2}} 16 - \log_{4} 32 \)
Answer Details
To solve this equation, we can use the logarithmic identity log(a) + log(b) = log(ab) and log(a) - log(b) = log(a/b).
Using this identity, we can simplify the equation:
log√24 + log1216 − log432
= log(24^(1/2)) + log(1216) - log(432)
= log(4^(1/2) * 6^(1/2)) + log(1216) - log(432)
= log(2*3) + log(1216) - log(432)
= log(2*3*1216/432)
= log(16)
Therefore, the answer is 2.5.
In summary, we use logarithmic identities to simplify the equation and find that the answer is 2.5.
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