A) a=2, 6 = 3
B) \[a=-2\], c=3
C) a=2, \[b=-3~~\]
D) a=3, b=2
Correct Answer: D
Solution :
If \[{{2}^{a}}+{{3}^{b}}=17\] \[{{2}^{a}}+{{3}^{b}}=8+9\] \[={{2}^{3}}+{{3}^{2}}\] Then, \[a=3\] and \[b=2\] and \[{{2}^{a+2}}-{{3}^{b+1}}=5\] \[4\times {{2}^{a}}-3\times {{3}^{b}}=32-27\] \[=4\times {{2}^{3}}-3\times {{3}^{2}}\]
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