Zie de
Voer in: `y_1=3*log(x)/(log(2))+16` .
Venster bijvoorbeeld: `[0, 200]xx[0, 50]` .
Voer in:
`y_2=38`
.
Snijden geeft:
`x~~161,27`
.
`3 *\ ^2log(x)+16` |
`=` |
`38` |
|
`\ ^2log(x)` |
`=` |
`22/3` |
|
`x` |
`=` |
`2^ (22 /3) ≈161,27` |
`text(D)_(f)=langle 0, →rangle` en `text(B)_(f)=ℝ` .
De verticale asymptoot is `x=0` .
`0 < x < 161,27`
De verticale asymptoot is `x=4` .
Voer in: `y_1=2+3*\ ^2log(x-4)` en `y_2=11` .
Venster bijvoorbeeld: `[4, 15]xx[text(-)15, 15]` .
`2 +3 *\ ^2log(x-4)` | `=` | `11` | |
`\ ^2log(x-4)` | `=` | `3` | |
`x-4` | `=` | `2^3` | |
`x` | `=` | `12` |
Bekijk de grafiek. De uitkomst is: `4 < x ≤ 12` .
`1 +4 *\ ^(0,5)log(x+5 )=text(-)3`
`\ ^(0,5)log(x+5 )` | `=` | `text(-)1` | |
`x+5` | `=` | `(1/2) ^(text(-)1)` | |
`x+5` | `=` | `2` | |
`x` | `=` | `text(-)3` |
`text(D)_(f)=langletext(-)5 ,→rangle` en `text(B)_(f)=ℝ` .
De verticale asymptoot is `x=text(-)5` .
`f(x)=text(-)3` voor `x=text(-)3` .
Voer in: `y_1=1+4*\ ^(0,5)log(x+5)` en `y_2=text(-)3` .
Venster bijvoorbeeld: `[text(-)5, 5]xx[text(-)5, 5]` .
Bekijk de grafiek. De uitkomst is: `text(-)5 < x≤text(-)3` .
De verticale asymptoot van de grafiek van `f` is `x=0` .
De verticale asymptoot van de grafiek van `g` is `x=2` .
`text(D)_(f)=langle 0, →rangle` en `text(D)_(g)=langle ←, 2 rangle`
`x=2-x` geeft `x=1` .
`1 < x < 2`
`\ ^6log(x)+\ ^6log(x-1)` | `=` | `1` | |
`\ ^6log(x(x-1))` | `=` | `1` | |
`(x-3)(x+2)` | `=` | `0` | |
`x` | `=` | `text(-)2 vv x=3` |
Alleen `x=3` voldoet.
`log( (2 x) / (x-1) )` | `=` | `2` | |
`(2 x) / (x-1)` | `=` | `10^2` | |
`(2x)/(x-1)` | `=` | `100` | |
`2 x` | `=` | `100 x-100` | |
`x` | `=` | `100/98=50/49` |
`\ ^3log(x-2)` | `=` | `1 +5 *\ ^3log(2)` | |
`\ ^3log(x-2)` | `=` | `\ ^3log(3)+\ ^3log(2^5)` | |
`\ ^3log(x-2)` | `=` | `\ ^3log(3)+\ ^3log(32)` | |
`\ ^3log(x-2)` | `=` | `\ ^3log(96)` | |
`x-2` | `=` | `96` | |
`x` | `=` | `98` |
`h` | `=` | `300 *log(q/5+20)` | |
`q/5+20` | `=` | `10^ (h/300)` | |
`q` | `=` | `5 *(10^ (h/300) -20)` | |
`q` | `=` | `5 *10^ (h/300) -100` |
`h` | `=` | `10 -5 *\ ^2log(q-4 )` | |
`\ ^2log(q-4 )` | `=` | `(h-10) /(text(-)5)=text(-)0,2 h+2` | |
`q-4` | `=` | `2^ (text(-)0,2 h+2)` | |
`q` | `=` | `2^ (text(-)0,2 h+2) +4` |
`x=text(-)4`
`text(D)_(f)=langle text(-)4, →rangle` en `text(B)_(f)=ℝ` .
`1 -3 *log(x+4 ) = 0` geeft `log(x+4) = 1/3` en `x=10^(1/3) - 4 = root[3](10) - 4` .
Grafiek: `text(-)4 < x < root(3)(10)-4` .
`x=1`
`text(D)_(g)=langle 1, →rangle` en `text(B)_(g)=ℝ` .
`text(-)10+2* \ ^(1/3)log(x-1) = text(-)14` geeft `\ ^(1/3)log(x-1) = text(-)2` en `x=(1/3)^(text(-)2) + 1 = 10` .
Grafiek: `1 < x≤10` .
`\ ^3log(x)=2 *\ ^3log(5 )=\ ^3log(5^2)` dus `x=25` .
`\ ^ (1/3) log(x)=\ ^ (1/3) log(5 )+\ ^ (1/3) log(2 ) = \ ^(1/3)log(2*5)` dus `x=10` .
`5 -\ ^2log(x)=0` geeft `\ ^2log(x)=5` en `x=2^5=32` .
`\ ^5log(x)=3 +4 *\ ^5log(3 ) = \ ^5log(5^3) + \ ^5log(3^4) = \ ^5log(5^3*3^4)` en dus `x=10125` .
`\ ^ (1/3) log(x)=\ ^ (1/3) log(5 )+\ ^ (1/3) log(2 -x)`
geeft
`\ ^ (1/3) log(x)=\ ^ (1/3) log(5(2 -x))`
.
Dus
`x = 10-2x`
en
`x=1 2/3`
.
`\ ^5log(x)=3 +4 *\ ^5log(x)` geeft `3*\ ^5log(x) = text(-)3` en dus `\ ^5log(x)=text(-)1` zodat `x=5^(text(-)1)=0,2` .
`text(D)_(f)=langle 0, →rangle`
`text(B)_(f)=ℝ`
.
De verticale asymptoot van `f` is `x=0` .
`text(D)_(g)=langle←, 4 rangle`
`text(B)_(g)=ℝ`
.
De verticale asymptoot van `g` is `x=4` .
`log(x) = text(-)1 + log(4-x)`
geeft
`log(x) = log(10^(text(-)1)) + log(4-x) = log(0,4-0,1x)`
.
Dus
`x = 0,4-0,1x`
en
`x=4/11`
.
Bekijk de grafieken van `f` en `g` . De uitkomst is: `0 < x≤ 4/11` .
`4/11 < x < 4`
`p` | `=` | `15 -\ ^3log(5 -q)` | |
`\ ^3log(5 -q)` | `=` | `15-p` | |
`5-q` | `=` | `3^(15-p)` | |
`q` | `=` | `5-3^(15-p)` |
`p` | `=` | `600 +15 *log(q/200)` | |
`log(q/200)` | `=` | `(p-600)/15` | |
`q/200` | `=` | `10^((p-600)/15)` | |
`q` | `=` | `200*10^((p-600)/15)` |
`log(10 A)=log(10 )+log(A)=1 +log(A)`
`10^(3,3)≈1995`
Vergelijkbaar bewijs als in
`D=152,7^@` , dus `16967` km.
`8,8=log(A/T)+1,66 *log(D)+3,30` geeft `log(A/T) + log(D^(1,66))=5,5` en dus `log(A/T * D^(1,66)) = 5,5` .
Dit betekent: `A/T * D^(1,66) = 10^(5,5)` en `D^(1,66) = 10^(5,5)*T/A` zodat `D ~~ (316227,766*T/A)^(1/(1,66))` .
Dit kun je schrijven als `D = 2057,09 * (T/A)^(0,60)` .
`p≈2057,09` en `q≈0,60` .
`x=6`
`x=0,2`
`x = 2/3`
`x = sqrt(1/2) = 1/2sqrt(2)`
( `x = text(-)sqrt(1/2)` voldoet niet.)
`text(D)_(f) = langle 0 ,→rangle` en `text(B)_(f) = ℝ` .
Verticale asymptoot van `f` : `x = 0` .
`text(D)_(g) = langle←,6 rangle` en `text(B)_(g) = ℝ` .
Verticale asymptoot van `g` : `x = 6` .
`x = 1/18`
`x gt 9841,5`
`x=5`
`x = 2`
`2 le x lt 6`
`D=10^0,75* (10^0,25) ^k-10`