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Category: Logarithms

log-3-a-1-log-4-a-8-a-

Question Number 175104 by blackmamba last updated on 19/Aug/22 $$\:\:\mathrm{log}\:_{\mathrm{3}} \left({a}+\mathrm{1}\right)=\mathrm{log}\:_{\mathrm{4}} \left({a}+\mathrm{8}\right) \\ $$$$\:{a}=? \\ $$ Answered by MJS_new last updated on 19/Aug/22 $${a}+\mathrm{8}=\mathrm{4}^{{x}} \wedge{a}+\mathrm{1}=\mathrm{3}^{{x}}…

Question-43187

Question Number 43187 by ajfour last updated on 08/Sep/18 Commented by ajfour last updated on 08/Sep/18 $${mass}\:{of}\:\left({toy}+{fuel}\right)=\:{M}+{m} \\ $$$${exhaust}\:{speed}\:\left({relative}\right)\:=\:{u} \\ $$$${friction}\:{coefficient}\:=\mu \\ $$$${Find}\:\left(\boldsymbol{{i}}\right)\:\boldsymbol{{maximum}}\:\boldsymbol{{velocity}} \\ $$$$\left(\boldsymbol{{ii}}\right)\:\boldsymbol{{Determine}}\:\boldsymbol{{how}}\:\boldsymbol{{far}}\:\boldsymbol{{can}}\:\boldsymbol{{it}}\:\boldsymbol{{go}}.…

If-a-b-and-c-are-in-a-GP-Prove-that-log-n-a-log-n-b-log-n-c-are-in-AP-

Question Number 42670 by Tawa1 last updated on 31/Aug/18 $$\mathrm{If}\:\:\mathrm{a},\:\mathrm{b}\:\mathrm{and}\:\mathrm{c}\:\:\mathrm{are}\:\mathrm{in}\:\mathrm{a}\:\mathrm{GP}.\:\:\mathrm{Prove}\:\mathrm{that}\:\:\:\mathrm{log}_{\mathrm{n}} \mathrm{a}\:,\:\:\mathrm{log}_{\mathrm{n}} \mathrm{b}\:\:,\:\:\mathrm{log}_{\mathrm{n}} \mathrm{c}\:\:\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP} \\ $$ Commented by maxmathsup by imad last updated on 31/Aug/18 $${we}\:{have}\:\:\frac{{b}}{{a}}\:=\frac{{c}}{{b}}\:\Rightarrow{b}^{\mathrm{2}}…

If-y-a-1-1-log-a-x-and-z-a-1-1-log-a-y-show-that-x-a-1-1-log-a-z-

Question Number 42549 by Tawa1 last updated on 27/Aug/18 $$\mathrm{If}\:\:\:\mathrm{y}\:=\:\mathrm{a}^{\frac{\mathrm{1}}{\mathrm{1}\:−\:\mathrm{log}_{\mathrm{a}} \mathrm{x}}} \:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\:\:\mathrm{z}\:=\:\mathrm{a}^{\frac{\mathrm{1}}{\mathrm{1}\:−\:\mathrm{log}_{\mathrm{a}} \mathrm{y}}} \:\:.\:\:\mathrm{show}\:\mathrm{that}\:\:\:\:\:\mathrm{x}\:=\:\mathrm{a}^{\frac{\mathrm{1}}{\mathrm{1}\:−\:\mathrm{log}_{\mathrm{a}} \mathrm{z}}} \\ $$ Answered by math1967 last updated on 27/Aug/18 $${log}_{{a}}…

Find-x-48log-a-4-5log-4-a-a-8-

Question Number 41797 by Tawa1 last updated on 12/Aug/18 $$\mathrm{Find}\:\mathrm{x}:\:\:\:\:\:\:\:\:\mathrm{48log}_{\mathrm{a}} \mathrm{4}\:\:+\:\:\mathrm{5log}_{\mathrm{4}} \mathrm{a}\:\:=\:\:\frac{\mathrm{a}}{\mathrm{8}} \\ $$ Answered by alex041103 last updated on 13/Aug/18 $${log}_{{b}} {a}=\frac{{lna}}{{lnb}}\:{and}\:{log}_{{a}} {b}=\frac{{lnb}}{{lna}} \\…

bemath-6-log-x-1-20-12x-x-7-36-gt-0-

Question Number 107318 by bemath last updated on 10/Aug/20 $$\:\:\:\:\:\circledcirc{bemath}\circledcirc \\ $$$$\mathrm{6}^{\mathrm{log}\:_{\left({x}−\mathrm{1}\right)} \left(\frac{\mathrm{20}−\mathrm{12}{x}}{{x}−\mathrm{7}}\right)} −\mathrm{36}\:>\mathrm{0} \\ $$ Answered by bobhans last updated on 10/Aug/20 $$\:\:\:\:\:\:\:\:\:\circledast\mathcal{BOBHANS}\circledast \\…