Posted by Austin on Thursday, January 3, 2013 at 11:05pm.
did you mean
log_{4} (x+2) = log_{4}(x^7)
or
log_{4}(x+2) = (log_{4}x)^7
or
....
your right side of the equation makes no sense
log lower 4(x+2)=log lower 4 7. does this make sense know? How do you make the lower sign to be able to get the 4 lower??
I wasn't worried about the lower case, I questioned the
log4^7
it makes no sense
that is similar to something like
√^7 or tan ^7
you take the log "of something" you can't just have have log
I had guessed that there would be an x of sorts, since the left side contained the variable x
it is written as you have it written the first time. I couldn't make out the question. It made no sense to me.
ok, if it is
log4 (x+2) = log4(x^7)
then x+2 = x^7 , (I "un-logged it)
x^7 = x+2 is a very nasty equation to solve, which is way beyond the scope of these kind of posts
You could use something like Newtons method
let y = x^7 - x - 2
dy/dx = 7x^6 - 1
new x = x - (x^7 - x - 2)/(7x^6 - 1)
pick any reasonable value for x
say x = 1 , (I know it does not work)
newx = 1 - (1-1-2)/(7-1)
= 1 - (-2/6) = 1.333333
make that your next x, and using a calculator
new x = 1.3333 - (....
= 1.22485...
...
newx = 1.1846
newx = 1.17975..
newx = 1.179693902
newx = 1.179693891
newx = 1.17969389 , wow, isn't that amazing