# logaritmische functies
image=0
n=$counter
F=f(x)\,\,=\,\,
Fa=f'(x)\,\,=\,\,
mytexsize=+2
R=$level
!if $level=0
    R=$counter
!endif    
    
pm=!randitem +,-
mp=!randitem +,-
s=!randitem 1,-1
keuze=!randitem 1,2
checkfile=exos/checkfile2.proc
ss=!record 7 of lang/remarks.$taal
question$n=$ss
exotext=!record 25 of lang/remarks.$taal
sometext=!record 26 of lang/remarks.$taal
exotext=<p><a onmouseover="return escape('$sometext')">$exotext
helptext=$empty

!if $R=1
    pm=!randitem +,-
    g=!randitem 2,3,4,5,6,7,8,9,10
    b=!randitem 2,3,4,5,6,7,8,9
    keuze=!randitem 1,2,3,4
    !if $keuze=1
	functie=log(x)/log($g)
	formula$n= $F ^{$g}\log \left( x \right)
    !else
	!if $keuze=2
	    functie=$b*log(x)/log($g)
	    formula$n= $F $b \cdot ^{$g} \log  \left( x \right)
	!else
	    !if $keuze=3
		functie=$b*log(x)/log(e)
		!if $lang=nl
		    formula$n= $F $b \cdot \ln  \left( x \right)
		!else
		    formula$n= $F $b \cdot ^{e} \log  \left( x \right)
		!endif
	    !else
		functie=log(x)/log($g) $pm $b
		formula$n= $F ^{$g}\log \left( x \right) $pm $b
	    !endif
	!endif
    !endif
    !goto READY
!endif

!if $R=2
    pm=!randitem +,-
    g=!randitem 2,3,4,5,6,7,8,9,10
    b=!randitem 2,3,4,5,6,7,8,9
    c=!randitem 1,2,3,4,5,6,7,8,9
    keuze=!randitem 1,2,3,4
    !if $keuze=1
	functie=log(x $pm $c )/log($g)
	formula$n= $F ^{$g}\log \left( x $pm $c \right)
    !else
	!if $keuze=2
	    functie=$b*log(x $pm $c)/log($g)
	    formula$n= $F $b \cdot ^{$g} \log  \left( x $pm $c \right)
	!else
	    !if $keuze=3
		functie=$b*log(x $pm $c )/log(e)
		!if $lang=nl
		    formula$n= $F $b \cdot \ln  \left( x  $pm $c  \right)
		!else
		    formula$n= $F $b \cdot ^{e} \log  \left( x  $pm $c  \right)
		!endif
	    !else
		functie=log(x $pm $c )/log($g) $pm $b
		formula$n= $F ^{$g}\log \left( x  $pm $c \right) $pm $b
	    !endif
	!endif
    !endif
    !goto READY
!endif

!if $R>2
    pm=!randitem +,-
    g=!randitem 2,3,4,5,6,7,8,9,10
    b=!randitem 2,3,4,5,6,7,8,9
    c=!randitem 2,3,4,5,6,7,8,9
    keuze=!randitem 1,2,3,4
    !if $keuze=1
	functie=log($c*x)/log($g)
	formula$n= $F ^{$g}\log \left( $c \cdot x \right)
    !else
	!if $keuze=2
	    functie=$b*log($c*x)/log($g)
	    formula$n= $F $b \cdot ^{$g} \log  \left( $c \cdot x \ \right)
	!else
	    !if $keuze=3
		functie=$b*log($c*x)/log(e)
		!if $lang=nl
		    formula$n= $F $b \cdot \ln  \left(  $c \cdot x \  \right)
		!else
		    formula$n= $F $b \cdot ^{e} \log  \left( $c \cdot x \  \right)
		!endif
	    !else
		functie=log($c*x)/log($g) $pm $b
		formula$n= $F ^{$g}\log \left(  $c \cdot x \ \right) $pm $b
	    !endif
	!endif
    !endif
!endif

:READY
sommen=!exec maxima factor(diff($functie ,x)); 
answer$n=!line 1 of $sommen	
answer$n=!replace internal log by ln in $(answer$n)
texanswer$n=!texmath $(answer$n)
texanswer$n=!replace internal log by ln in $(texanswer$n)
texanswer$n=$Fa $(texanswer$n)


!exit
