Logarithms!

Common logarithms

100

log₂2=x

x=1

200

log₅x=4

x=625

300

log₅125=3 is equivalent to 5³=125

True or false?

True

400

log(x+2)=3

998

500

log(x+2)-log(x-1)=3

x=334/333 or x=1 1/333

natural logarithms

100

ln2=x

e^x=2

200

lne²

2

300

lne³+lne⁴

7

400

20lna - 4lnb

lna²⁰/b⁴

500

ln(x+1)-ln(x+3)=6

x=-17/5

Solve by change base

100

2^x+1=4^2x+2

x=-1

200

2^2x+1=4^x+1

no solution

300

8^x+2=16^9x-1

10/33

400

64^x+2=8^x+3

x=-1

500

125^x+4=25^2x+3

x=6

Solve with inverse

100

log₄(x+1)=3

x=63

200

1^x = 2^x+1

no solution

300

1^x+1=4^x+4

no solution

400

5^x=4^x+3

x=(3log4)/(log5-log4)

500

6^x = 5^x+6

x = log(6) / (log(6) - log(5)

General - here you can take points off

100

log₂x=4

x=16

200

lne⁴

4

300

4^x+1=2^x+2

x=0

400

3^x+4=9^3x+6

x=-8/5

500

log(x+4)-log(x-2)=2

x=68/33 or 2 2/33