Exponents and Radicals

Solve for x:

4(8^x)-21(4^x)+21(2^x)=4

View the solution

Exponents and Radicals Solution

8^x=(2^x)³, and 4^x=(2^x)². Now, if we allow u to equal 2^x, we can solve an equation in u:

4u³-21u²+21u-4=0

(4u-1)(u-1)(u-4)=0

u = 2^x= 1/4, 1, or 4

x = 0, 2, or -2

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