Logarithm Review

Evaluating Logarithms

100

log₁₂144

X=2

200

Log₃81

X=4

300

Log₂(1/32)

X=-5

400

Log₅5⁷

X=7

500

Log₉9^(2x+1)

X=-1

Rewriting Logarithms

100

Expand the expression: log(3x²)

log(3)+2log(x)

200

Write as a single logarithm: log(x)+2log(y)

log(xy²)

300

Expand the expression: ln(x^3/y)

3log(x)-log(y)

400

Write as a single logarithm: 3ln(a)-ln(b)-ln(c)

ln(a³/bc)

500

Expand the expression: log(x⁴sqrt(y)/z³)

4log(x)+1/2log(y)-3log(z)

Solve by Rewriting Forms

100

3^x=9

X=2

200

log₇x=2

x=49

300

9^x-4=6.28

X=4.84

400

log_b12=1

X=12

500

8^x-2=2^x-4

X=1

Solving base e equations

100

e^x=9

X=2.2

200

e^x=1.1

X=0.095

300

e^-x=31

X=-3.43

400

3e^x+1=4

X=0

500

4+e^x=19

X=2.71

Solving equations with natural logarithms

100

ln6x=2

X=1.23

200

ln4X=3

X=5.02

300

ln(-2X)=7

X=-548.32

400

ln(X-6)=1

X=8.72

500

ln(2X)+ ln(4)=8

X=372.6