Anyone know how to do logarithmic calculations Here are some

Anyone know how to do logarithmic calculations. Here are some problems I can\'t figure out how to do. log b 4 = 1/2(that\'s supposed to be one half). log y 9=2. ln 2=x. ln 5x=3. log16 x^1/2=3/4. log 16 x= -3/4

Solution

logb4 =1/2

logab = loga +logb

logb + log4=1/2

logb +0.6 =0.5

logb = 0.5-0.6

logb =-0.1

b = 10^-0.1

b=0.8

logy9 =2

logy + log9 =2

logy + 0.95 =2

logy = 2-0.95

logy =1.045

y = 10^(1.045)

y=11.1

ln2=x

x= 0.7

ln5x =3

ln5+lnx =3

1.61 +lnx=3

lnx = 3-1.61

lnx =1.39

x=e^(1.39)

x=4.01

log16x^1/2 =3/4

log16 +logx^1/2 =3/4

loga^m =mloga

log16 +1/2 logx =3/4

1.2 +1/2 logx =3/4

1/2logx =0.75 -1.2

1/2logx =-0.45

logx=-0.9

x = 10^(-0.9)

x=0.125

log16x =-3/4

log16 +logx =-0.75

logx =-0.75 -1.2

logx=-1.95

x=0.011