Logs

Changing forms

100

log₄64=3

4³=64

200

8³=512

log₈512=3

300

log 1/10=-1

10^-1=1/10

400

16²=256

log₁₆256=2

500

log_1/7(1/343)=3

(1/7)³=1/343

Evaluate or Simplify

100

Log1,000

3

200

Log10000^x

4x

300

log₃1/9

-2

400

8^log₈^2x

2x

500

Log100^x

2x

Expand/Condense

100

5lnx - 12lny

ln(x⁵/y¹²)

200

9log₅x + 3log₅y + 3log₅z

log₅(x⁹y³z³)

300

log₃((zx)⁶/y)²

12log₃z +12log₃x - 2log₃y

400

log₅(uv³)⁴

4log₅u + 12log₅v

500

log₉x + 5log₉y - 6log₉z

log₉((xy⁵)/z⁶)

Find the following

100

if ln2=0.70 and ln4=1.39 Find ln8

2.09

200

if ln2=0.70 and ln4=1.39 Find ln16

2.78

300

if ln2=0.70 and ln4=1.39 Find ln1/2

-0.69

400

if ln2=0.70 and ln4=1.39 Find ln32

3.49

500

if ln2=0.70 and ln4=1.39 Find ln128

4.9

Inverse

100

y=log₅x

5^x=y

200

y=log_1/2x-4

(1/2)^x+4=y

300

y=log (x-1)

10^x+1=y

400

y=log_1/26x

(1/6)(1/2)^x=y

500

y=log_1/5(x+3)-2

(1/5)^x+2-3=y