Problem: Through the use of theorems of logarithmslogab+logbc+logcd−logaydx\operatorname{logarithms} \log \dfrac{a}{b}+\log \dfrac{b}{c}+\log \dfrac{c}{d}-\log \dfrac{a y}{d x}logarithmslogba+logcb+logdc−logdxay can be reduced to:
Answer Choices:
A. logyx\log \dfrac{y}{x}logxy
B. logxy\log \dfrac{x}{y}logyx
C. 111
D. 000
E. loga2yd2x\log \dfrac{a^{2} y}{d^{2} x}logd2xa2y Solution:
loga−logb+logb−logc+logc−logd−loga−logy+logd+logx=log(x/y)\log a-\log b+\log b-\log c+\log c-\log d-\log a-\log y+\log d+\log x=\log (x / y) loga−logb+logb−logc+logc−logd−loga−logy+logd+logx=log(x/y)