Question 1163251: Pls help me. Given that logx^256=2 find log8^(1over x) Thanks Found 3 solutions by Theo, MathTherapy, ikleyn:Answer by Theo(13342) (Show Source):
start with 2 = log(x^256)
this is true if and only if:
10^2 = x^256
take the 256th root of both sides of this equation to get:
(10^2)^(1/256) = (x^256)^(1/256)
solve this equation for x to get:
x = (10^2)^(1/256) = 1.018151722
you now want to find log(8^(1/x))
set y = that to get:
y = log(8^(1/x))
since x = 1.018151722, that becomes:
y = log(8^(1/1.018151722)
solve for y to get:
y = .8869895986
that should be your solution, if i understood the problem correctly.
If you meant: , then READ on!
------ Converting to EXPONENTIAL form
------ EXPONENTS are equal and so are the BASES
Now, what's needed is: . If it's , then you're on your own, but should be able to figure it out, if you follow below!
-------- Substituting 16 for x
--- Letting the value of be "c."
-------- Converting to EXPONENTIAL form
4c = 3 ------ BASES are equal and so are the EXPONENTS
