Question

Can someone help please

Answer 1

`x=-4y`

`y=-(x)/(4) }`

Explanation:

Solve the following equation for both x and y.

`2^((x+4y))=1\\\\\\\hrule`

Apply the following natural log rule for exponents:

`\ln(x^n)=n\ln(x)`

`2^((x+4y))=1\\\\\\\\\Longrightarrow \ln(2^((x+4y)))=\ln(1); \ \text{Recall} \ \ln(1)=0\\\\\\\\\Longrightarrow (x+4y)\ln(2)=0\\\\\\\\\Longrightarrow \boxed{x\ln(2)+4y\ln(2)=0}`

Solving for the variable "x."

`x\ln(2)+4y\ln(2)=0\\\\\\\\\Longrightarrow x\ln(2)=-4y\ln(2)\\\\\\\\\Longrightarrow x=(-4y\ln(2))/(\ln(2))\\\\\\\\\therefore \boxed{\boxed{x=-4y}}`

Solving for the variable "y."

`x\ln(2)+4y\ln(2)=0\\\\\\\\\Longrightarrow 4y\ln(2)=-x\ln(2)\\\\\\\\\Longrightarrow x=(-x\ln(2))/(4\ln(2))\\\\\\\\\therefore \boxed{\boxed{y=-(x)/(4) }}`

Thus, the problem is solved.