Question

вычислите log2 2/3+log4 9/4

Answer 1

log2 2/3+log4 9/4 = log2 2/3+1/2log2 9/4 = log2 2/3+log2 3/2
от суммы логарифмов перейдем к логарифму произведения:
log2 2/3+log2 3/2 = log2 (2/3*3/2) = log2 1 = 0

Answer 2

$log_{2} frac{2}{3} +log_{4} frac{9}{4}= log_{2} frac{2}{3} +log_{2^2} frac{9}{4}=log_{2} frac{2}{3} + frac{1}{2} log_{2} frac{9}{4}=log_{2} frac{2}{3} +log_{2} sqrt{frac{9}{4}}=$$=log_{2} frac{2}{3} +log_{2} {frac{3}{2}}=log_{2}( frac{2}{3} *frac{3}{2}})=log_{2} 1=0$