1. Start by adding 15 to both sides of the equation.
log_2x+log_2x-15=4
log_2x+log_2x=19
2. Use the logarithmic property, log_color(purple)b(color(red)m*color(blue)n)=log_color(purple)b(color(red)m)+log_color(purple)b(color(blue)n) to simplify the left side of the equation.
log_2(x*x)=19
log_2(x^2)=19
3. Use the logarithmic property, log_color(purple)b(color(purple)b^color(orange)x)=color(orange)x, to rewrite the right side of the equation.
log_2(x^2)=log_2(2^19)
4. Since the equation now follows a "log=log" situation, where the bases are the same on both sides, rewrite the equation without the "log" portion.
x^2=2^19
5. Solve for x.
sqrt(x^2)=sqrt(2^(19)
x=2^(19/2)
color(green)(|bar(ul(color(white)(a/a)x~~724.08color(white)(a/a)|)))
Note that although when you take the square root of 2^19, a negative solution should also be produced, it is not actually a solution because if you substitute x=-2^(19/2) back into the original equation, you will notice that you end up taking the logarithm of a negative number, which is not possible.
