Natural Logs

Defining "e"

100

e^x = 60

solve for x

x = ln(60)

200

e^x+1 = 30

solve for x

x = ln(30) - 1

300

lne^x = ln28

solve for x

x = ln(28)

400

4ln(x+2) = 32

solve for x

x = e⁸-2

500

ln(x+2)-ln(x-2)=1

solve for x

x=(-2-2e)/(1-e)

Log to exponential

100

ln(6)=x

e^x=6

200

e^x-2=12

ln(12)=x-2

300

ln(9)=3x

e^3x=9

400

y=ln(x²+3)

e^y=x²+3

500

4e^2x+2=16

ln(4)=2x

How to expand and condense logs

100

Expand ln(³√x²).

²/₃lnx

200

Condence 6log₆2 + 3log₆x + log₆(4x+1) − log₆(2x−1)

log₆(64x³(4x+1)(2x−1))log₆(64x³(4x+1)(2x−1)).

300

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

ln 9x² / y³

400

Expand log₆ (36 √x / ⁴√y 

2+ 1/2 log₆ (x) - 1/4 log₆ (y)

500

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 −2r = 4

−27.2991

500

ln (m + 8) = −2

−7.8647

Kerchak

100

what is the name of Yzma's partner in emperor's new groove (who later got a movie of his own)

KRONK

200

Main antagonist in ratatouille

Skinner

300

Whats the name of the fat guy in mars needs moms

Gribble (George Ribble)

400

Whats the name of the mountain monster in Tarzan 2

ZUGOR

500

In what movie is India Golf 99 mentioned

The incredibles