No 4-17 tolong bantu

No. 4
a=0,111111...
Kalikan 10
10a=1,11111...
Kedua ruas dikurangi a
10a-a=1,11111... -0,111111...
9a=1
a=1/9
b=0,333333
Kalikan 10
10b=3,333333...
Kedua ruas dikurangi b
10b-b=3,333333... -0,3333...
9b=3
b=3/9=⅓
^alogb=^1/9 log ⅓=^3^-2 log 3^-1=-1/-2.³log3=½. 1=½
No. 5
²log(√2+1+√2-1)
=²log 2√2
=²log2¹.2^½
=²log 2^3/2
=3/2.²log2=3/2.1=3/2
No.6
Log y¹.y^½ + log x^½ + log x²y per log xy
=log y^3/2.x^½.x²y per log xy
=log x^5/2.y^5/2 per log xy
=log (xy)^5/2 per log xy
=^xy log (xy)^5/2
=5/2.^xy log xy
=5/2.1=5/2
No. 7
2¹=³log ²log x
³log ²log x=2
²log x=3²
²log x =9
x=2^9=512
No. 8
Log 2x=1
2x=10¹
2x=10
x=5
^25 log 5=^5² log 5¹=½. ^5log 5=½. 1=½
No. 9
^5log75=^5 log 3.5²
=^5log 3 + 2.^5log 5
=a+2