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Question: 2^x 3^y = 72, what is x + y?                                                                       Solution: x=3 and y=2/ 2^x 3^y= 72 = 2^3 * 3^2= 72                                                   So, if x=3 and y=2 then, 3+2 =5                                                                               The answer: x+y= 5

apologiabiology

solve for x and solve for y

2^x3^y=72

divide both sides by 3^y
2^x=72/(3^y)

take the log₂ of both sides

x=log₂(72/(3^y))
x=log₂72-log₂3^y

x=log₂(182^2)-ylog₂3

x=log₂18+log₂2^2-ylog₂3

x=log₂18+2log₂2-ylog₂3

x=log₂18+2-ylog₂3



solve for y

2^x3^y=72

divide both sides by 2^x

3^y=72/(2^x)

take log₃ of both sides

y=log₃(72/(2^x))

y=log₃72-log₃2^x

y=log₃(3^28)-xlog₃2

y=log₃3^2+log₃8-xlog₃2

y=2log₃3+log₃8-xlog₃2

y=2+log₃8-xlog₃2


so

x+y=log₂18+2-ylog₂3+2+log₃8-xlog₃2

x+y=log₂18-ylog₂3+log₃8-xlog₃2+4

not sure how to simplify further

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