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Išspręskite lygtis:

1. 5^2x =125;

2. | x - 2 | = 5.

Sprendimas:

1.

5^^(2*x) =
125

5^^(2*x) = 125 $5^{(2*x)}$ = $125$

5^^(2*x) = 5* 5* 5 $5^{(2*x)}$ = $5\cdot 5\cdot 5$

5^^(2*x) = 5^³ $5^{(2*x)}$ = $5^{3}$

log(₅, 5^^(2*x)) = log(₅, 5^³) $log_{5}(5^{(2*x)})$ = $log_{5}(5^{3})$

( 2* x) = log(₅, 5^³) $(2\cdot x)$ = $log_{5}(5^{3})$

( 2* x) = 3 $(2\cdot x)$ = $3$

2* x = 3 $2\cdot x$ = $3$

x =

3

/ 2

$x$ = $\frac{3}{2}$

x = 1.5 $x$ = $1.5$

Atsakymas: x = 1.5

2.

| x-2 | =
5

| x-2 | = 5 $|x-2|$ = $5$

x-2 = 5 $x-2$ = $5$

x = 5+2 $x$ = $5+2$

x = 7 $x$ = $7$

x-2 = -5 $x-2$ = $-5$

x = 2-5 $x$ = $2-5$

x = -3 $x$ = $-3$

Atsakymas: x = -3 ir x = 7

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