Question

8^x+1 = 16^y+2,1/2^3+x= 1/4^3y

Answer 1

Good Morning

$(8) {}^{(x + 1)} = (16) {}^{(y + 2)} \\ \\ 2 {}^{3(x + 1)} = 2 {}^{4(y + 2)} \\ on \: comparing \: powers \: of \: 2 \: we \: get\: \\ \\ 3(x + 1) = 4(y + 2) \\ \\ 3x - 4y = 5 \: \: ...Equation \: \: \: (i) \\ \\ and \\ \\ (1 \div 2) {}^{(3 + x)} = (1 \div 2) {}^{6y} \\ on \: comparing \: powers \: of \: (1 \div 2) \: we \: get \\ \\ 3 + x = 6y \\ \\ 6y - x = 3 \: \: ...Equation \: \: \: (ii) \\ \\ solve \: \: both \: the \: equations \: we \: have \: \\ \\ y = 1 \: \: and \: \: x \: = 3$

Answer 2

So, y=1 and x=3

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