16^2*(16^-3)^2*4^38
--------------------------- = 16^x what is x
(16^(-1)*2^12)
+130518 Here's another approach
16^2*(16^-3)^2*4^38
--------------------------- = 16^x what is x
(16^(-1)*2^12)
Notice that 2^12 = (2^2)^6 = 4^6
And 4^38 / 2^12 = 4^38 / 4^6 = 4^32 = (4^2)^16 = 16^16 ..... so we have
[16^2 * [ (16)^(-3)]^2 * 16^16] / 16^(-1) =
[16^(2) [16^(-6) * 16^16] / 16^(-1) =
16^(12) / 16^(-1) =
16^13 so x must = 13
Here is a very simple and straightforward way of doing it:
Solve for x over the real numbers:
4503599627370496 = 16^x
Reverse the equality in 4503599627370496 = 16^x in order to isolate x to the left hand side.
4503599627370496 = 16^x is equivalent to 16^x = 4503599627370496:
16^x = 4503599627370496
Perform the prime factorization of the left hand side.
16^x = 2^(4 x):
2^(4 x) = 4503599627370496
Perform the prime factorization of the right hand side.
4503599627370496 = 2^52:
2^(4 x) = 2^52
Equate exponents.
Equate exponents of 2 on both sides:
4 x = 52
Solve the linear equation.
All equations give x = 13 as the solution:
Answer: |
| x = 13
