19 uždavinys

Sprendimas:

$$log_{5}(x-7) = 0$$

$$log_{5}(x-7) = log_{5}(5^{0})$$

$$log_{5}(x-7) = log_{5}(1)$$

$$x-7 = 1$$

$$x = 8$$

x = 8 patenka į apibrėžimo sritį.

Atsakymas: x = 8

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Sprendimas:

$$sin(x)+sin(2\cdot x) = 0$$

$$sin(x)+2\cdot sin(x)\cdot cos(x) = 0$$

$$sin(x)\cdot (1+2\cdot cos(x)) = 0$$

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$$sin(x) = 0$$

$$x = \pi\cdot k$$

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$$1+2\cdot cos(x) = 0$$

 $$2\cdot cos(x) = -1$$

 $$cos(x) = -\frac{1}{2}$$

 $$x = \frac{2\cdot \pi}{3}+2\cdot \pi\cdot k$$

 $$x = -\frac{2\cdot \pi}{3}+2\cdot \pi\cdot k$$

Atsakymas: $$x = \pi\cdot k$$ ir $$x = \frac{2\cdot \pi}{3}+2\cdot \pi\cdot k$$ bei  $$x = -\frac{2\cdot \pi}{3}+2\cdot \pi\cdot k$$