CÂU 8. Rút gọn a) log_(2)5cdot ln2+4ln5 b) (log_(7)9)/(log_(7)4)+5log_(2)sqrt (3) c) log_(5)7.log_(2)5.log_(3)4 d) (log_(5)16)/(log_(5)3)+(5)/(log_(2)sqrt (3))

【Giải thích】: a) Áp dụng quy tắc logarit: $log_{a}b * log_{b}a = 1$ và $log_{a}a = 1$, ta có $log_{2}5 * ln2 + 4ln5 = log_{2}5 + 4log_{2}5 = 5log_{2}5 = log_{2}25 = 2$.<br />b) Áp dụng quy tắc logarit: $log_{a}b/c = log_{a}b - log_{a}c$ và $log_{a}\sqrt{b} = \frac{1}{2}log_{a}b$, ta có $\frac {log_{7}9}{log_{7}4} + 5log_{2}\sqrt {3} = log_{7}9 - log_{7}4 + \frac{5}{2}log_{2}3 = log_{7}\frac{9}{4} + \frac{5}{2}log_{2}3 = log_{7}2.25 + log_{2}3\sqrt{5} = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.25 + log_{2}15 = log_{7}2.