Natural Logs

Defining "e"

100

e^x = 60

solve for x

x = 4.0943

200

e^x+1 = 30

solve for x

x = 2.4012

300

lne^x = ln28

solve for x

x = 3.3322

400

4ln(x+2) = 32

solve for x

x = 2978.958

Log to exponential

100

e^x-2=12

ln(12)=x-2

200

ln(9)=3x

e^3x=9

300

y=ln(x²+3)

e^y=x²+3

400

4e^2x+2=16

ln(4)=2x

How to expand and condense logs

100

Expand ln(³√x²).

²/₃lnx

200

Condence 2(ln x+ ln 3) - 3 ln y

ln 9x² / y³

300

Expand log₆ (36 √x / ⁴√y 

2 log₆ (6) + 1/2 log₆ (x) - 1/4 log₆ (y) OR

2 + 1/2 log₆ (x) - 1/4 log₆ (y)

400

2ln (x+3) + ln (x-3) - ln(x² - 9)

ln (x+3)

How the properties of exponents and Natural logs work together to simplify expressions

100

e ^-4x + 8 = 35

-0.824

200

4e ^{r + 5} = 29

-3.019

300

-9.3e ^10b = -67

0.1975

400

ln (m + 8) = −2

−7.8647