Question

Find the solution of the logarithmic equation:
ln(x+8)+ln(x–8)=0

Im not sure how to approach this one. I tried moving the ln(x-8) to the other side and solving for x and that did not work. I also tried putting everything as an exponent to e. please help! thanks

Answer 1

that is ln of product
ln (x^2-64) = 0
e^ln anything = anything
so
x^2-64 = e^0 = 1
x^2 -65 = 0
x = +/- sqrt 65
but ln of negative is undefined
so
x = +sqrt(65)