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Category: Logarithms

1-2-log-4-36-log-6-64-

Question Number 177360 by jlewis last updated on 04/Oct/22 $$\mathrm{1}/\mathrm{2}\:{log}_{\mathrm{4}} \mathrm{36}\:×{log}_{\mathrm{6}} \mathrm{64} \\ $$ Answered by TheHoneyCat last updated on 08/Oct/22 $$=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}_{\mathrm{4}} \left(\mathrm{4}×\mathrm{9}\right)×\mathrm{log}_{\mathrm{6}} \left(\mathrm{6}×\mathrm{9}\right) \\…

4-16-x-4-5-2-2x-13-

Question Number 177361 by jlewis last updated on 04/Oct/22 $$\mathrm{4}\left(\mathrm{16}^{\left({x}+\mathrm{4}\right)} \:×\:\mathrm{5}.\mathrm{2}^{\mathrm{2}{x}} =\mathrm{13}\right. \\ $$ Answered by a.lgnaoui last updated on 04/Oct/22 $$\:\mathrm{2}^{\mathrm{2}} \left(\mathrm{2}^{\mathrm{4}} \right)^{\left({x}+\mathrm{4}\right)} ×\mathrm{5}.\mathrm{2}^{\mathrm{2}{x}}…

X-and-Y-are-playing-a-game-Initially-there-are-three-bundles-of-matches-consisting-of-2021-2022-and-2023-pieces-Each-player-in-his-turn-chooses-a-bundle-B-and-removes-a-positive-number-of-the

Question Number 177113 by LOSER last updated on 01/Oct/22 $${X}\:{and}\:{Y}\:{are}\:{playing}\:{a}\:{game}.\: \\ $$$${Initially}\:{there}\:{are}\:{three}\:{bundles}\:{of}\: \\ $$$${matches},\:{consisting}\:{of}\:\mathrm{2021},\:\mathrm{2022}\: \\ $$$${and}\:\mathrm{2023}\:{pieces}.\:{Each}\:{player}\:{in}\:{his}\: \\ $$$${turn}\:{chooses}\:{a}\:{bundle}\:{B}\:{and}\:{removes}\: \\ $$$${a}\:{positive}\:{number}\:{of}\:{the}\:{matches}\:{of}\:{B}\: \\ $$$${such}\:{that}\:{the}\:{number}\:{of}\:{pieces}\:{of}\: \\ $$$${bundles}\:{still}\:{form}\:{an}\:{arithmetic}\: \\…

Plz-solve-log-17-92-1-9-

Question Number 45781 by Junaid555 last updated on 16/Oct/18 $$\:\:\:{Plz}\:{solve} \\ $$$$\:\:\:\:\boldsymbol{{log}}\:\left(\mathrm{17}.\mathrm{92}\right)^{−\frac{\mathrm{1}}{\mathrm{9}}} \\ $$ Answered by hassentimol last updated on 19/Oct/18 $$ \\ $$$$\mathrm{The}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{the}\:\mathrm{following}\:: \\…