Find the exact solutions, in their simplest form, to the equations: ln(2y+5)=2+ln(4–y)

The first aim of the question to collect all the like terms together. In this example the 'ln(4-y)' must be subtracted from both sides. Now we must recall the log rules and realise the 'ln' function can be condensed. The log rule which this question concerns 'ln(A) - ln(B) = ln(A/B)'. The equation now becomes one ln function equals to 2. Now if we raise both sides with an exponential the ln function on the left side of the equation will cancel. This is because the ln function is inverse of the exponential function. Now we just simply multiply the denominator on both sides and collect the y terms. Now we just make y the subject of the equation and the question is solved.