10 uždavinys

Lygties 9^x+1 =3^4x-2 sprendinys yra:

A - 1 B 0 C 1 D 2

Sprendimas:

9^^(x+1) =
3^^(4*x-2)

9^^(x+1) = 3^^(4*x-2) $9^{(x+1)}$ = $3^{(4*x-2)}$

3^^(2*(x+1)) = 3^^(4*x-2) $3^{(2*(x+1))}$ = $3^{(4*x-2)}$

log(₃, 3^^(2*(x+1))) = log(₃, 3^^(4*x-2)) $log_{3}(3^{(2*(x+1))})$ = $log_{3}(3^{(4*x-2)})$

( 2* (x+1)) = log(₃, 3^^(4*x-2)) $(2\cdot (x+1))$ = $log_{3}(3^{(4*x-2)})$

( 2* (x+1)) = ( 4* x-2) $(2\cdot (x+1))$ = $(4\cdot x-2)$

2* (x+1) = ( 4* x-2) $2\cdot (x+1)$ = $(4\cdot x-2)$

2* (x+1) = 4* x-2 $2\cdot (x+1)$ = $4\cdot x-2$

2* x+ 2* 1 = 4* x-2 $2\cdot x+2\cdot 1$ = $4\cdot x-2$

2* 1 = 4* x- 2* x-2 $2\cdot 1$ = $4\cdot x-2\cdot x-2$

2* 1+2 = 4* x- 2* x $2\cdot 1+2$ = $4\cdot x-2\cdot x$

4 = 4* x- 2* x $4$ = $4\cdot x-2\cdot x$

4 = 2* x $4$ = $2\cdot x$

/ 2

= x $\frac{4}{2}$ = $x$

2 = x $2$ = $x$

$9^{(x+1)}$ = $3^{(4*x-2)}$

$3^{(2*(x+1))}$ = $3^{(4*x-2)}$

$2\cdot (x+1)$ = $4\cdot x-2$

$2\cdot x+2\cdot 1$ = $4\cdot x-2$

$4$ = $2\cdot x$

$2$ = $x$

Atsakymas: D