Rovnice podle funkcí
1) Zjednodušte výrazy:
3x ⋅ 2x + 1 = 2 ⋅ 36x + 2
3 ⋅ 2x + 2x = 32
3x - 2 ⋅ 3x - 1 + 3x - 2 - 2 ⋅ 3x - 3 = 30
e11x + 8 = 1
( 2 7 )3x + 2 = ( 7 2 ) 1 - x 4
0,42x · 2,5 = ( 2 5 )x + 4
3 9 x + 4 + 9 · 3x = 2 3
20 ⋅ 2x - 2x + 1 = 3x + 2 - 3x
2) Nahraďte proměnnou v daném výrazu konkrétní hodnotou:
4log3(2x - 1) = 16
log2[log3(log4x² + 10)] = 2
log3(3x² - 2x) = log3(- 4x + 5)
log13[log5(log3x + 3)] = 0
1 - 2log x 3 + log x = 4 - 2log x 5 + log x
log24 - log2x + (log22x)² = 9
log28x² + log²22x² = 8
logx3 + 3log3x9 = 6logx²3
log4x - 2log0,25x = 6
3) Nahraďte proměnné v daném výrazu konkrétními hodnotami:
4sin²(x) – tg²(x) = 1
sin²(x) = sin(x) ⋅ cos(x) ⋅ √3
2 √3 · tg( x 2 + π 4 ) = - 2√3 3
√3 · sin( x 2 ) - sin(x) = 0
2cos²(x) – 3 = 3sin(x)
2sin²(x) + sin(x) – 1 = 0
cos(3x) = 0
2sin²(x) − 3 = 2 cos(x) ⋅ sin(x)