Question 286068
Solve for x:
{{{Log[2](5-x)+Log[2](5+x) = 4}}} Apply the "product rule" for logarithms: {{{highlight_green(Log[b](M)+Log[b](N) = Log[b](M*N))}}}
{{{Log[2]((5-x)(5+x)) = 4}}} Simplify the left side.
{{{Log[2](25-x^2) = 4}}} Recall the definition of the logarithm: 
"The logarithm of a number (or an expression) is the power to which the base must be raised to equal that number (or expression)" 
Rewrite the above equation accordingly:
{{{2^4 = 25-x^2}}} Simplify.
{{{16 = 25-x^2}}} Rearrange into a standard quadratic equation.
{{{x^2-9 = 0}}} Factor the left side.
{{{(x+3)(x-3) = 0}}} Apply the "zero product rule" 
{{{x+3 = 0}}} or {{{x-3 = 0}}} therefore:
{{{x = -3}}} or {{{x = 3}}}