Question 1010579
i don't get -4 except as an intermediate result.


here's what i get.


start with:


4 - log4(x+8) = 8


multiply both sides of this equation by -1 to get:


-4 + log4(x+8) = -8


add 4 to both sides of this equation to get:


log4(x+8) = -4


that's the only place i get a -4.


log4(x+8) = -4 if and only if 4^(-4) = x+8


since 4^(-4) = 1/256, the equation becomes:


1/256 = x + 8


solve for x to get x = -8 + 1/256 which results in:


x = -2047/256.


it does not appear this can be simplified any further than that, so that is the value in fraction format.


to see if that value is correct, replace x in the original equation with it.


you will get:


4 - log4(x+8) = 8 becomes:


4 - log4(-2047/256 + 8) = 8


since 8 = 2048/256, this equation becomes:


4 - log4(-2047/256 + 2048/256) = 8


combine like terms to get:


4 - log4(1/256) = 8.


log4(1/256) = log(1/256)/log(4) = -4


equation becomes:


4 - (-4) = 8


combine like terms to get 8 = 8.


this confirms the solution is correct.


your solution is that x = -2047/256.


that's equivalent to -(7 + 255/256) which can also be written as -7 - 255/256.


in decimal format, that would be x = -7.99609375 rounded to 8 decimal places.