1. Bring all the logs to the left side of the equation.
log(x+6)=1-log(x-5)
log(x+6)+log(x-5)=1
2. Use the log 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 rewrite the left side of the equation.
log((x+6)(x-5))=1
3. Use the log property, log_color(purple)b(color(purple)b^color(orange)x)=color(orange)x, to rewrite the right side of the equation.
log((x+6)(x-5))=log(10)
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+6)(x-5)=10
5. Expand the brackets.
x^2+x-30=10
6. Subtract 10 from both sides.
x^2+x-40=0
7. Use the quadratic formula to solve for x.
color(darkorange)(a=1)color(white)(XXXXXX)color(teal)(b=1)color(white)(XXXXXX)color(violet)(c=-40)
x=(-b+-sqrt(b^2-4ac))/(2a)
x=(-(color(teal)1)+-sqrt((color(teal)1)^2-4(color(darkorange)1)(color(violet)(-40))))/(2(color(darkorange)1))
x=(-1+-sqrt(1+160))/2
color(green)(|bar(ul(color(white)(a/a)x=(-1+-sqrt(161))/2color(white)(a/a)|)))
