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Question Number 92196 by I want to learn more last updated on 05/May/20

$$2^{\mathrm{x}}+3^{\mathrm{y}}=72$$$$2^{\mathrm{y}}+3^{\mathrm{x}}=108$$$$\mathrm{Please}\mathrm{am}\mathrm{not}\mathrm{getting}\mathrm{correct}\mathrm{answer}\mathrm{for}$$$$\mathrm{this}\mathrm{question}\mathrm{using}\mathrm{a}\mathrm{method}\mathrm{proposed}.$$

Commented by john santu last updated on 05/May/20

$$\mathrm{aproximation}$$$$x=4.1506283099$$$$y=3.6349521185$$

Commented by I want to learn more last updated on 05/May/20

$$\mathrm{Yes}\mathrm{sir}.\mathrm{but}\mathrm{workings}\mathrm{to}\mathrm{get}\mathrm{it}.$$$$\mathrm{Am}\mathrm{using}\mathrm{a}\mathrm{method}\mathrm{by}\mathrm{sir}\mathrm{jagol}\mathrm{but}$$$$\mathrm{not}\mathrm{giving}\mathrm{correct}\mathrm{answer}$$

Commented by MJS last updated on 05/May/20

$${\mathrm{there}}^{\prime }\mathrm{s}\mathrm{no}\mathrm{possible}\mathrm{path},\mathrm{you}\mathrm{can}\mathrm{only}$$$$\mathrm{approximate}$$$$2^x+3^y=72\Rightarrow y=\frac{\ln (72-2^x)}{\ln 3}$$$$2^y+3^x=108\Rightarrow y=\frac{\ln (108-3^x)}{\ln 2}$$$$72-2^x>0\wedge 108-3^x>0\iff x<\frac{\ln 108}{\ln 3}\approx 4.262$$$$\frac{\ln (72-2^x)}{\ln 3}=\frac{\ln (108-3^x)}{\ln 2}$$$$\mathrm{now}\mathrm{use}\mathrm{a}\mathrm{calculator}$$

Commented by MJS last updated on 05/May/20

$$...\mathrm{if}\mathrm{the}\mathrm{method}\mathrm{you}\mathrm{use}\mathrm{gives}\mathrm{a}\mathrm{wrong}\mathrm{result}$$$$\mathrm{the}\mathrm{method}\mathrm{is}\mathrm{wrong}$$

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