Question 83

The real root of the equation $$2^{6x} + 2^{3x + 2} - 21 = 0$$ is

Solution

Let $$2^{3x}$$ = v

$$2^{6x} + 2^{3x + 2} - 21 = 0$$

= $$v^2+4v-21=0$$

=(v+7)(v-3)=0

v=3, -7

$$2^{3x}$$ = 3 or $$2^{3x}$$ = -7(This can be negated)

3x=$$\log_23$$

x=$$\log_23$$/3

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