solve the following equations for x
question 9
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let 2^x = t
and we know that a^m*a^n = a^m+n
so given equation can be written as
(2^x)^2 -2^x*2^3 + 2^4 = 0
t^2 -8t +16 =0
t^2-4t-4t+16 = 0
t(t-4)-4(t-4) = 0
(t-4)(t-4) = 0
(t-4)^2 = 0
t-4 = 0
t = 4
so 2^x = 4 = 2^2
x=2
therefore x=2
and we know that a^m*a^n = a^m+n
so given equation can be written as
(2^x)^2 -2^x*2^3 + 2^4 = 0
t^2 -8t +16 =0
t^2-4t-4t+16 = 0
t(t-4)-4(t-4) = 0
(t-4)(t-4) = 0
(t-4)^2 = 0
t-4 = 0
t = 4
so 2^x = 4 = 2^2
x=2
therefore x=2
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