12 uždavinys
Išspręskite lygtis:
1. 52x =125;
2. | x - 2 | = 5.
Sprendimas:
1.
5^(2*x) =
125
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 =
$$x$$ = $$\frac{3}{2}$$
| 3 |
| / 2 |
x = 1.5$$x$$ = $$1.5$$
Atsakymas: x = 1.5
2.
| x-2 | =
5
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