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Question Number 140863 by mathdanisur last updated on 13/May/21

$$1+\sqrt{3^{\mathit{a}}}=2\sqrt{2^{\mathit{a}}}$$

Commented by mr W last updated on 13/May/21

$$a=0or2$$

Commented by mathdanisur last updated on 13/May/21

$$thanksdearSirsolutionsplease$$

Commented by mr W last updated on 13/May/21

$$thereisnoformulatocalculatethe$$$$solution.inthisspecialcaseyoucan$$$$‘‘{see}^{″}thesolutionisa=0or2,because$$$$theyareobvious.$$$$ifthequestionis1+\sqrt{3^{\mathit{a}}}=3\sqrt{2^{\mathit{a}}}then$$$$thesolutionisnotobvious.ithink$$$$thereisnowaytogettheexact$$$$solution.$$$$throughsuchquestionsonecan$$$$learnnothingandonecanteach$$$$nothing.$$

Commented by mathdanisur last updated on 13/May/21

$$thankyoudearSir★$$

Answered by ajfour last updated on 14/May/21

$$p^2=3^a{q}^2=2^a$$$$\Rightarrow 2\ln p=a\ln 3$$$$2\ln q=a\ln 2$$$$p=\frac{3q}{2}$$$$1+p=2q$$$$1+3q=2q$$$$\Rightarrow q=-1$$$$\Rightarrow 2^a=1\Rightarrow a=0$$$$p=-3$$$$3^a=9\Rightarrow a=2$$

Commented by prakash jain last updated on 14/May/21

$$\mathrm{How}\mathrm{did}\mathrm{you}\mathrm{get}\mathrm{p}=\frac{3\mathrm{q}}{2}?$$

Commented by bramlexs22 last updated on 14/May/21

$$\iff \mathrm{a}=\mathrm{a}$$$$\iff \frac{\cancel{2ln}\mathrm{p}}{\ln 3}=\frac{\cancel{2ln}\mathrm{q}}{\ln 2}$$$$\iff \ln \mathrm{p}=\frac{\ln 3.\ln \mathrm{q}}{\ln 2}$$$$\Rightarrow \ln \mathrm{p}=\frac{\ln {\mathrm{q}}^{\ln 3}}{\ln 2}$$$$\Rightarrow \ln \mathrm{p}=\ln {\mathrm{q}}^{\ln 3^{\frac{1}{\ln 2}}}$$$$\Rightarrow \mathrm{p}={\mathrm{q}}^{\ln 3^{\frac{1}{\ln 2}}}$$

Commented by prakash jain last updated on 14/May/21

$$\mathrm{It}{\mathrm{isn}}^{\prime }\mathrm{t}\mathrm{same}\mathrm{as}\mathrm{p}=\frac{3\mathrm{q}}{2}$$

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