Natural Logarithmic Equation ln (x+30) + ln x = ln 31
Given logarithmic equation is `ln(x+30)+lnx=ln31`
We know that `lnx+lny=ln(xy)`
As `lnx=lnyrArrx=y` .
or, `x=1` and `x=-31.`
As logarithm for negative numbers is not defined. We can discard x=-31.
So x=1 is the desired solution.
The equation ln (x+30) + ln x = ln 31 has to be solved for x.
ln (x+30) + ln x = ln 31
Use the rule ln x + ln y = ln(x*y)
ln((x+30)*x) = ln 31
=> (x+30)*x = 31
=> x^2 + 30x - 31 = 0
=> x^2 + 31x - x - 31 = 0
=> x(x + 31) - 1(x + 31) = 0
=> (x - 1)(x + 31) = 0
=> x = 1 and x = -31
As the logarithm of a negative number is not defined, eliminate x = -31
The solution of the equation is x = 1