#var3=x
#checkfile=exos/checkfile6.proc
checkfile=$checkdir/number.proc
arglist=x
# answer must be 'x=123'
image=0
math=0
questiontype=0
!set n=$counter
!if $level =0
    R=$counter
!else
    R=$level
!endif        

exotitle=!record 3 of lang/remarks.$taal
#@ Vergelijkingen met Exponenten
question$n=!record 62 of lang/remarks.$taal
#@ Los op:<br><small><em>bereken dus de waarden van x</em><br>noteer bij meerdere oplossingen iets als:<br><em>x</em>=1 en <em>x</em>=2/3 of zo...<br>en bij breuken graag het antwoord vereenvoudigen.</small>
!if $R=1
    keuze=!randitem 1,0
    pm=!randitem 1,-1
    # g^(ax+b) = 1 => ax+b =0 => x=-1*(b)/(a)
    a=!randint 2,20
    a=$[$pm*$a]
    b=!randitem 1,2,3,4,5,6,7,8,9,10
    g=!randitem 2,3,4,5,6,7,8,9,10,e
    !if $keuze=0
	formula$n=$g^{($a*x + $b)} = 1
	answer$n=!exec pari (-1*$b)/($a)
	texanswer$n= -> $g^{($a*x + $b)} = $g^0 -> $a*x + $b = 0 -> x = $(answer$n)
    !else
	formula$n=$g^{($a*x - $b)} = 1
	answer$n=!exec pari ($b)/($a)
	texanswer$n= -> $g^{($a*x - $b)} = $g^0 -> $a*x - $b = 0 -> x = $(answer$n)
    !endif
 !exit
!endif 

!if $R=2
    # g^((x+b)(x+a)) = 1 => (x+b)(x+a)=0 => x=-a,-b    
    cijfers=!shuffle 1,2,3,4,5,6,7,8,9,10
    a=!item 1 of $cijfers
    b=!item 2 of $cijfers
    g=!randitem 2,3,4,5,6,7,8,9,10,e
    keuze=!randitem 0,1,2
    !if $keuze=0
	formula$n=$g^{((x+$a)(x+$b))} = 1
	answer$n=$[-1*$a],$[-1*$b]
	texanswer$n=$g^{((x+$a)(x+$b))} = $g^0 -> (x+$a)(x+$b)= 0 -> x_1=$[-1*$a]  x_2=$[-1*$b]
    !else
    
	!if $keuze=1
	    formula$n=$g^{((x-$a)(x-$b))} = 1
	    answer$n=$a,$b
	    texanswer$n= -> $g^{((x-$a)(x-$b))} = $g^0 -> (x-$a)(x-$b)= 0 -> x_1=$a V x_2=$b
	!else
	    formula$n=$g^{((x+$a)(x-$b))} = 1
	    answer$n=$[-1*$a],$b
	    texanswer$n= -> $g^{((x+$a)(x-$b))} = $g^0 -> (x+$a)(x-$b)= 0 -> x_1=$[-1*$a] V x_2=$b
	!endif
    !endif
 !exit
!endif 

!if $R=3
    # g^(x^2+abx + ab) = 1     
    cijfers=!shuffle 1,2,3,4,5,6,7,8,9,10
    a=!item 1 of $cijfers
    b=!item 2 of $cijfers
    g=!randitem 2,3,4,5,6,7,8,9,10,e
    pm=!randitem -,+
    mp=!randitem -,+
    functie=!exec pari (x $mp $a)*(x $pm $b)
    formula$n=$g^{($functie)} = 1
    answer$n=$[-1*($mp $a)],$[-1*($pm $b)]
    texanswer$n= -> $g^{($functie)} = $g^0 -> $functie = 0 -> (x $mp $a)*(x $mp $b) = 0 -> x_1=$[-1*($mp $a)] V x_2=$[-1*($pm $b)] 
 !exit
!endif 

!if $R>3
    # g^(x^2+abx + ab +c) = g^(c)     
    cijfers=!shuffle 1,2,3,4,5,6,7,8,9,10
    a=!item 1 of $cijfers
    b=!item 2 of $cijfers
    c=!randitem 2,3,4,5,6,7,8,9,10
    g=!randitem 2,3,4,5,6,7,8,9,10,e
    pm=!randitem -,+
    mp=!randitem -,+
    functie=!exec pari (((x $mp $a)*(x $pm $b)) + $c)
    formula$n=$g^{($functie)} = $g^$c
    answer$n=$[-1*($mp $a)],$[-1*($pm $b)]
    texanswer$n= -> $g^{($functie)} = $g^$c -> $functie = $c -> (x $mp $a)*(x $mp $b) = 0 -> x_1=$[-1*($mp $a)] V x_2=$[-1*($pm $b)] 
 !exit
!endif 
