Question

高一数学【对数】

已知log【a】ab=1/p，则log【ab】a/b=_________.

Answer 1

解：

log【a】(ab)=1/p

∴(lga+lgb)/lga=1/p

1+(lgb/lga)=1/p

lgb/lga=(1-p)/p

∴log【ab】(a/b)

=[lga-lgb]/lg(ab)

=[lga-lgb]/[lga+lgb]

=[1-(lgb/lga)]/[1+(lgb/lga)]

=[1-(1-p)/p]/[1+(1-p)/p]

=[p-(1-p)]/[p+(1-p)]

=[2p-1]/1

=2p-1

谢谢