Exponentials & Logs

same base

100

3^x+2=243

x=3

200

2^x+1=32

x=4

300

4^x+3=256

x=1

400

8^x-2=512

x=5

500

5^2x+2=625

x=1

log properties

100

log_b(MN)

log_b(M)+log_b(N)

200

log₆(x/2)

log₆x-log₆2

300

log(3²)

2log3

400

ln8+ln2

ln10

500

log6mn

log6+logm+logn

solving exponentials

100

6^4x-3=1

x=3/4 

200

9^x-3=9^4x

x=-1

300

e^x-7=1.5

exact: x=ln1.5+7

approx: 7.41

400

4^2x=64

exact: log₄64/2

approx: 1.5

500

10^6x+2=232

exact: log232-2/6

approx: 0.061

solving logs

100

5+ln2x=4

x=0.1839

200

log₂(5x+7)=5

x=5

300

log₂x+log₂3=4

16/3

400

log₃x-log₃10=3

x=200

500

log₆x+log₆(x+1)=1

x=2 

log basics

100

Convert to exponential form

log₁₅225=2

15²=225

200

Convert to exponential form

log₃27=3

3³=27

300

Evaluate

log₆216

3

400

Convert to logarithmic form

2⁷=128

log₂187=7

500

 Evaluate ln(1/sqrte^3)

-3/2