Question

Log 11(2x-1) = 1-log11(x+4). Find the value of x showing detailed reasoning?

Answer 1

`x=-5 or 3/2` but -5 is not a real solution

Explanation:

`Log₁₁(2x-1)+Log₁₁(x+4)=1`
`Log₁₁(2x^2+7x-4)=1`
`11^1=2x^2+7x-4`
`2x^2+7x-15=0`
`2x^2+10x-3x-15=0`
`2x(x+5)-3(x+5)=0`
`x=-5 or 3/2`