Log Functions & Geometric Sequences

log 1

100

What is the range of f(x)= - ln x?

All Real Numbers

200

What is the domain of f(x)=ln x? 

x > 0 

300

What is the asymptote of f(x)=ln x? 

x=0

400

Solve log₅(125)=x

x=3

500

Solve 8^x=24

x=1.528

log 2

100

Find the approximate value of log₂(7) to the nearest thousandths. 

2.807

200

What is the x-intercept of ln(x)?

(1,0)

300

Describe all the translations to f(x) = log x to tranform  the function into g(x)= - 2 log (x + 3) + 4

x-axis reflection, vertical stretch of 2, left 3, up 4

400

Describe all the translations to f(x) = log x to tranform  the function into g(x)= .2 log (x - 3) - 4

vertical compression of .2, right 3, down 4

500

Describe the end behavior of f(x) = - ln x

x-->0     y--> oo

x--> oo   y--> -oo

geometric

100

Is  1, 4, 16, 64... a geometric sequence? 

If yes identify a₁ and r

Yes a₁=1 and r = 4

200

Write the recursive form of the sequence 1, 4, 16, 64

           1             n=1

a_n=

           r* a_n-1     n>1

300

Write the explicit form of the sequence 1, 4, 16, 64

a_n = 1*4^(n-1)

400

Find the sum.   

6

E       5(2)^x-1

x=1

315

500

Find the number of terms for the series  1+4+16+64+256+...+16,384. 

And find the sum of the series.

8 terms

21,845

log 3

100

Find the exact value of log₂(7) 

 log 7 / log 2

200

Expand the following: 

log(2x³/y)

log2+3logx-logy

300

Rewrite the following as a single logarithm.

2 log x + 3log y - log z

log(x²y³)/z

400

Find the inverse of the following:

f(x)=2 log (x + 3) + 4

f(x)^-1 =10^(x-4)/2  -  3

500

Find the inverse of the following:

f(x)=2e^x+4-6

f(x)^-1=ln((x+6)/2)-4

Final Jeopardy

500

The number of the last lesson in the workbook was?

6.7