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Guest Dec 11, 2014

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Write 4^x as (2²)^x = 2^2x

Then 4^x - 2^x = 56 becomes 2^2x - 2^x = 56 which is: 2^2x - 2^x - 56 = 0

Now, factor: (2^x - 8)(2^x + 7) = 0

Either: 2^x - 8 = 0 ---> 2^x = 8 ---> x = 3

Or: 2^x + 7 = 0 ---> 2^x = -7 (impossible for real numbers)

geno3141 Dec 11, 2014

geno3141 · Answer 1 · 2014-12-11T01:03:48

Write 4^x as (2²)^x = 2^2x

Then 4^x - 2^x = 56 becomes 2^2x - 2^x = 56 which is: 2^2x - 2^x - 56 = 0

Now, factor: (2^x - 8)(2^x + 7) = 0

Either: 2^x - 8 = 0 ---> 2^x = 8 ---> x = 3

Or: 2^x + 7 = 0 ---> 2^x = -7 (impossible for real numbers)