Question Number 137764 by byaw last updated on 06/Apr/21 $$\mathrm{If}\:\mathrm{log}_{\mathrm{2}} \mathrm{3}={a}\:\mathrm{and}\:\mathrm{log}_{\mathrm{3}} \mathrm{7}={b},\:\mathrm{express} \\ $$$$\mathrm{log}_{\mathrm{42}} \mathrm{56}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{a}\:\mathrm{and}\:{b} \\ $$ Answered by EnterUsername last updated on 06/Apr/21 $${log}_{\mathrm{2}}…
Question Number 6373 by sanusihammed last updated on 25/Jun/16 $${If}\:\:\:\:\mathrm{9}{log}_{{a}} ^{\mathrm{5}} \:\:=\:\:{log}_{\mathrm{5}} ^{{a}} \\ $$$${find}\:{the}\:{value}\:{of}\:{a}\: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{SOLUTION} \\ $$$$ \\ $$$$\mathrm{9}{log}_{{a}} ^{\mathrm{5}} \:\:=\:\:{log}_{\mathrm{5}}…
Question Number 6346 by sanusihammed last updated on 24/Jun/16 Commented by prakash jain last updated on 25/Jun/16 $$\mathrm{If}\:{a},{b},{c}\in\mathbb{R} \\ $$$$\mathrm{then}\:\mathrm{there}\:\mathrm{are}\:\mathrm{no}\:{a},{b},{c}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{log}\:\frac{{a}}{{b}−{c}}=\mathrm{log}\:\frac{{b}}{{c}−{a}}=\mathrm{log}\:\frac{{c}}{{a}−{b}} \\ $$$${let}\:{there}\:\exists\:{a},{b},{c}\in\mathbb{R}\:\mathrm{satisfying}\:\mathrm{the}\:\mathrm{condition} \\…
Question Number 6111 by Kasih last updated on 14/Jun/16 $${log}^{\mathrm{2}} {x}+{logx}^{\mathrm{2}} −\mathrm{3}=\mathrm{0}\:,\:{x}=? \\ $$ Answered by prakash jain last updated on 14/Jun/16 $$\mathrm{log}\:{x}={u} \\ $$$${u}^{\mathrm{2}}…
Question Number 5949 by sanusihammed last updated on 06/Jun/16 $${Solve}\:{simultaneously} \\ $$$$ \\ $$$${a}\:+\:{b}\:=\:\mathrm{9}\:\:\:…………\:{equation}\:\left({i}\right) \\ $$$${log}_{\mathrm{2}} {a}\:+\:{log}_{{b}} \mathrm{2}\:\:=\:\:\mathrm{5}\:\:\:\:\:……….\:{equation}\:\left({ii}\right) \\ $$$$ \\ $$$${please}\:{help}. \\ $$ Terms…
Question Number 5592 by Rasheed Soomro last updated on 21/May/16 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{positive}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{for} \\ $$$$\mathrm{which}\:\mathrm{9x}^{\frac{\mathrm{2}}{\mathrm{3}}} +\mathrm{4x}^{−\frac{\mathrm{2}}{\mathrm{3}}} =\mathrm{37}\:. \\ $$ Answered by prakash jain last updated on 21/May/16…
Question Number 5580 by Rasheed Soomro last updated on 21/May/16 $$\mathrm{Given}\:\mathrm{that}\:{p}^{{n}} =\mathrm{16}{p},\:\mathrm{express}\:\mathrm{log}_{\mathrm{2}} {p}\: \\ $$$$\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{n}\:. \\ $$ Answered by FilupSmith last updated on 21/May/16 $${p}^{{n}}…
Question Number 5579 by Rasheed Soomro last updated on 21/May/16 $$\mathrm{Without}\:\mathrm{using}\:\mathrm{a}\:\mathrm{calculator},\:\mathrm{evaluate} \\ $$$$\left(\mathrm{log}\:\mathrm{5}\right)^{\mathrm{2}} +\mathrm{log}\:\mathrm{2}\:\mathrm{log}\:\mathrm{50} \\ $$ Answered by FilupSmith last updated on 21/May/16 $$\mathrm{log}\:{x}\:=\:\mathrm{log}_{\mathrm{10}} {x}…
Question Number 5569 by Rasheed Soomro last updated on 20/May/16 $$\mathrm{The}\:\mathrm{result}\:“\mathrm{log}\:\mathrm{xy}=\mathrm{log}\:\mathrm{x}+\mathrm{log}\:\mathrm{y}''\:\mathrm{is}\:\mathrm{not} \\ $$$$\mathrm{always}\:\mathrm{true}!\:\mathrm{Give}\:\mathrm{a}\:\mathrm{pair}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of} \\ $$$$\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{result}\:\mathrm{will}\:\mathrm{not}\:\mathrm{hold}. \\ $$ Commented by Yozzii last updated on 20/May/16 $$\left({x},{y}\right)=\left(−\mathrm{1},\mathrm{2}\right)…
Question Number 71016 by mr W last updated on 10/Oct/19 $$\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+…\right)\right)\right)=? \\ $$ Answered by mr W last updated on 11/Oct/19 $$\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+…\right)\right)\right)={x} \\ $$$$\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+{x}\right)={x} \\…