Question 894348
log(1) - 6log(x) = 9


you want to combine the logs into 1.


since 6log(x) = log(x^6), your equation becomes:


log(1) - log(x^6) = 9


since log(1) - log(x^6) = log(1/x^6), your equation becomes:


log(1/x^6) = 9


since log(1/x^6) = 9 if and only if 10^9 = 1/x^6, your equation becomes:


10^9 = 1/x^6


multiply both sides of this equation by x^6 to get:


10^9 * x^6 = 1


divide both sides of this equation by 10^9 to get:


x^6 = 1/10^9


take the 6th root of both sides of this equation to get:


x = (1/10^9)^(1/6)


solve for x using your calculator to get = .0316227766


let's see if this is a good solution.


your original equation is log(1) - 6*log(x) = 9


replace x with .0316227766 and you get:


log(1) - 6*log(.0316227766) = 9


simplify to get:


0 - 9 = 9 which results in 9 = 9 which confirms your solution is good.