Question

Anyone know how to do this ?

Answer 1

$\log_b\sqrt{\dfrac{57}{74}}=\log_b\left(\dfrac{57}{74}\right)^\frac{1}{2}=\dfrac{1}{2}\log_b\dfrac{57}{74}=\dfrac{1}{2}(\log_b57-\log_b74)\\\\=\dfrac{1}{2}\log_b57-\dfrac{1}{2}\log_b74\\-----------------------------\\Used:\\\\\sqrt{a}=a^\frac{1}{2}\\\\\log_ab^n=n\log_ab\\\\\log_a\dfrac{m}{n}=\log_am-\log_an\\\\a(b-c)=ab-ac$