Solving Logs and Exponents
Change Base Formula
Log Theorums
100

log100,000

5

100

log(base 4)(x)=7

4^7=x

100

ln(e)^3

3

200

log10+log100

3

200

log(base x)(71)=301

x^301=71

200

write as sum or difference of logarithms

log(10/30)

log(10)-log(30)

300

$12,000 is invested into a company that earns a 3.2% interest compounded continuously. How many years will it take to get to $18,000.

12.67 years

300

10^1=x

log(x)=1

300
Write as a single Logarithm

ln(x-1)+ln(x+1)-2ln(x^2-3)

ln(x^2-1)/(x^2+3)^2

400

3log(2x-1)=10

x=1077

400

P^x=y

log(base P)(y)=x

400

logbase5(7)

1.2091


500

f(x)=ln(2x-3)+1

x= 1/2e + 3/2

500

log(base 12)(x)=1/60

12^1/60=x

500

ln(sqrt x+3 3rdrtx-4)/(x+1)^4

write as sum or difference of Logarithms 

ln(x1/2+3)+ln(x1/3-4)-4ln(x+1)

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