Find the solution of the logarithmic equation \\ln(x+7) + \\ln(x-7) =0 in terms of logarithms, or correct to four decimal places. Your answer is Solution ln(x+7)+ln(x-7)=0 ln[(x+7)(x-7)]=0 10^0 = (x+7)(x-7) 1 = (x+7)(x-7) 1 = x^2 - 49 x^2 = 50 x = sqrt(50) = sqrt(25*2) = sqrt(25)*sqrt(2) x = 5*sqrt(2) (reject the negative root) hope this helps!.

1. Find the solution set of the following system of inequalities?
Does this have to be done with a graph? Very confused.
Solution
This can be done by drawing the graphs of the functions.
The red graph represent [y = (x+8)/2] and green graph shows [y = -x+1] .
What we need is [y<(x+8)/2] which is the area below the red graph and [y>= -x+1] which is the
area above green graph.
[(x+8)/2 = -x+1]
[x = -2]
The interception point is (-2,3)
The required area is the area to the right of the interception point between the graphs.