Evaluate log√24+log1216−log432

Evaluate $lo{g}_{\sqrt{2}}4+lo{g}_{\frac{1}{2}}16-lo{g}_{4}32$

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.