Category: Logarithms

Question Number 167215 by Avijit007 last updated on 09/Mar/22 Answered by MikeH last updated on 09/Mar/22 $${\log }_{b}a\times {\log }_{c}b\times {\log }_{a}c=$$$$\:\frac{\mathrm{1}}{\cancel{\mathrm{log}_{{a}} {b}}}\:×\:\frac{\cancel{\mathrm{log}_{{a}} {b}}}{\mathrm{log}_{{a}} {c}}×\:\mathrm{log}_{{a}}…

Question Number 101553 by bobhans last updated on 03/Jul/20 $$\mathrm{solve}\mathrm{the}\mathrm{inequality}$$$${({}^3\log x+2)}^{5x+1}⩾{({}^3\log x+2)}^{3-3x}$$ Answered by bramlex last updated on 03/Jul/20 $$\rightarrow\left(\mathrm{log}\:_{\mathrm{3}}…

Question Number 35899 by imamu222 last updated on 25/May/18 $$Evaluate{log}_{\sqrt{2}}4+{log}_{1/2}16-{log}_{4}32$$ Commented by Cheyboy last updated on 26/May/18 $${log}_{\sqrt{\mathrm{2}}} \mathrm{4}+{log}_{\mathrm{1}/\mathrm{2}} \mathrm{16}−{log}_{\mathrm{4}}…

Question Number 166687 by cortano1 last updated on 25/Feb/22 $$\log {}_{(2\mathrm{x}-1)}(\mathrm{x}+1)>\log {}_{(4-2\mathrm{x})}(\mathrm{x}+1)$$$$\mathrm{x}=?$$ Commented by Nimatullah last updated on 25/Feb/22 $${p} \…

Question Number 100720 by bemath last updated on 28/Jun/20 Commented by 1549442205 last updated on 28/Jun/20 $$$$$$\mathrm{one}\mathrm{other}\mathrm{way}:\mathrm{the}\mathrm{conditions}\mathrm{for}\mathrm{the}$$$$\mathrm{inequality}\mathrm{is}\mathrm{defined}\mathrm{as}:\frac{\mathrm{x}-5}{5}>0\iff \mathrm{x}>5$$$$\mathrm{Since}\:\mathrm{log}_{\mathrm{8}} \frac{\mathrm{x}−\mathrm{5}}{\mathrm{5}}=\mathrm{log}_{\mathrm{2}} \left(\frac{\mathrm{x}−\mathrm{5}}{\mathrm{5}}\right)^{\frac{\mathrm{1}}{\mathrm{3}}}…