Begin by moving both of the #log# terms to the left hand side.
#log(x+8) - log(x-10) = 1#
Now we can use the division rule for logarithms to combine both terms into one. The division rule states that;
#log(m/n) = log(m) - log(n)#
Letting #m=x+8# and #n=x-10#, we get;
#log((x+8)/(x-10)) = 1#
Since we are working with a common #log# it is base ten. That means that the part inside of the parenthesis is equal to #10# raised to the power of the right hand side, or;
#10^1 = (x+8)/(x-10)#
Now we just need to do some algebra to solve for #x#. First, multiply both sides by #(x-10)#.
#10(x-10) = x+8#
Now multiply the #10# through the parenthesis.
#10x - 100 = x + 8#
Subtract #x# and add #100# to both sides.
#9x = 108#
Finally, divide both sides by #9# to find #x#.
#x = 12#
