Question

Solve the equation
`16^(x)-3(4^(x+1))=28`. Write your answer in the form
`(ln a)/(ln b)`, where a and b are integers.

Answer 1

Hi,

Explanation:

Let's assume y=4^x

`16^x-3*4^(x+1)=28\\\\4^(2x)-3*4^(x+1)=28\\\\(4^(2x))/(4) -3*4^x-7=0\\\\(y^2)/(4) -3y-7=0\\\\\Delta=9+4*(1)/(4) *79+7=16=4^2\\\\y=(3-4)/((2)/(4)) \Longrightarrow\ \ y=-2 : impossible\\\\or\ y=(3+4)/((2)/(4))=14\\ \\4^(x)=14\\\\x*ln(4)=ln(14\\\\\boxed{x=(ln(14))/(ln(4)) }`