1. (²log5+³log5)׳⁶log0,2 ÷(²log5.³log5) =

(log5/log2 + log5/log3)(log0,2/log36)÷(log5/log2 . log5/log3) =

log5.log0,2.log2.log3/(log2.log36.log5.log5) + log5.log0,2.log2.log3/(log3.log36.log5.log5) =

log0,2.log3/(log5.log36) + log0,2.log2/(log36.log5) =

log5⁻¹.log3/(log5.log6²)+ log5⁻¹.log2/(log6².log5)=

-log5.log3//(log5.2log6)+ -log5.log2/(2log6.log5)=

-½log3/log6 - ½log2/log6 =

-½(log3 + log2)/log6 =

-½log6/log6 =

-½

2. 2ײlog a = ²log(3a-4) +1

2loga/log2 = log(3a-4)/log2 + log2/log2

2loga/log2 =( log(3a-4)+log2)/log2

2loga = log(3a-4)+log2

loga² = log(2(3a-4))

a² = 2(3a-4)

a²-6a +8= 0

(a-4)(a-2) = 0

a = 4 atau a = 2

3. log (logx) + log2 = 1

log (2logx ) = 1

2logx = 10¹

2logx = 10

logx = 5

x = 10⁵

x = 100000

4. ³log25.⁶log81.⁴log2/(³log36 - ³log4) =

³log5².⁶log3⁴.⁴log2/

(³log36/4) =

4⁶log3.³log5.⁴log2/³log9 =

4⁶log5.⁴log2/³log3² =

4⁶log5.⁴log2/(2(1)) =

2⁶log5.⁴log2 =

2⁶log5.½²log2 =

⁶log5.1 =

⁶log5

5. ²log3 = a

³log7 = b

⁴²log56 =?

42 = 2×3×7

56 = 2³×7

⁴²log56 =

³log56/ ³log42 =

³log(2³.7)/³log(2.3.7) =

(³log2³+³log7)/(³log2+³log3+³log7) =

(3³log2 + ³log7)/(³log2+1+³log7) =

(3/²log3 + ³log7)/(1/²log3 + 1 + ³log7) =

((3/a) +b )/((1/a) +1 + b)