Question

8 to the power of x+3=16 to the power of x-1

Answer 1

`\bf 8^(x+3)=16^(x-1)\qquad \begin{cases} 8=2\cdot 2\cdot 2\\ \qquad 2^3\\ 16=2\cdot 2\cdot 2\cdot 2\\ \qquad 2^4 \end{cases}\implies (2^3)^(x+3)=(2^4)^(x-1) \\\\\\ 2^(3(x+3))=2^(4(x-1))\impliedby \begin{array}{llll} \textit{since the bases are the same}\\ \textit{the exponents must also be the same} \end{array} \\\\\\ 3(x+3)=4(x-1)\implies 3x+9=4x-4\implies 9+4=4x-3x \\\\\\ \boxed{13=x}`

Answer 2

8^x+3=16^x+1, 2^3(x+3)=2^4(x+1), 2^3x+9=2^4x+4, same bases. 3x+9=4x+4, 3x-4x=4-9, -x=-5, x=5