Solving Exponential Equation (sol'n includes complex values of X)@KasyannoEZMath

This tutorial video shows how to solve the given exponential equation. The solution included the complex values of X.

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[artandata]

at video time 8:04, you don't need to use log! since 4^x=64 is 4^x=4^3. then as bases are identical x=3 (the which is also the result for log64/log4 but found in an easier way. regards

[thorinpalladino]

While you can leave the base as 4 I find it much easier to manipulate the numbers using base 2. This may be due to me using binary for so long, so other people may find the extra step of converting to base 2 to be more of a hassle than it is worth.

4160 can be rewritten as 64+4096. Which can be rewritten as 2^6 + 2^12.
So the equation can be rewritten as 2^(2X) + 2^(4X) = 2^6 + 2^12.
Converting back to base 4 makes the answer very obvious: 4^X +4^(2X) + 4^3 + 4^6
X=3

[kfjfkeofitorhf]

X=3
4^3+16^3=4^3=(2^2)^3=2^6
16^3=4^2^3=(2^2)^2^3=2^12
2^6+2^12=4160

[walterwen]

Solving Exponential Equation: 4^x + 16^x = 4160; x = ?
4^x + 16^x = 4^x + 4^2x = 4160 = (4^3)(65) = (4^3)(1 + 64)
= (4^3)(1 + 4^3) = 4^3 + 4^6; x = 3