SOLUTION: 4-log4(x+8)= 8 , the end answer is -4, but I keep getting 1 may you please explain. Sidenote: It is log base 4 Thanks so much!!! :D

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 4-log4(x+8)= 8 , the end answer is -4, but I keep getting 1 may you please explain. Sidenote: It is log base 4 Thanks so much!!! :D       Log On


   

Question 1010579: 4-log4(x+8)= 8 , the end answer is -4, but I keep getting 1 may you please explain. Sidenote: It is log base 4
Thanks so much!!! :D
Found 3 solutions by Alan3354, josgarithmetic, Theo:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
4-log4(x+8)= 8 , the end answer is -4, but I keep getting 1 may you please explain. Sidenote: It is log base 4
------------
4-log%284%2C%28x%2B8%29%29+=++8
log%284%2C%28x%2B8%29%29+=++-4
x%2B8+=+4%5E%28-4%29+=+1%2F256
x = 1/256 - 8 = -2047/256

Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
4-log%284%2C%28x%2B8%29%29=8

-log%284%2C%28x%2B8%29%29=4

log%284%2C%28x%2B8%29%29=-4

4%5E%28-4%29=x%2B8

x%2B8=1%2F4%5E4

x=-8%2B1%2F256

x=1%2F256-2048%2F256

highlight%28highlight%28highlight%28x=-2047%2F256%29%29%29
about -7.996094

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.