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Logarithm <--> Exponential Form

1

Turn log₃9=2 into exponential form.

3²=9

2

Turn 5^-2 = 1/25 into logarithmic form

log₅1/25 = -2

3

Turn log_1/636 = -2 into exponential form

1/6^-2 = 36

4

Turn x^(m+3)=g into logarithmic form

log_xg=m+3

5

Turn log_x(p-5)=k into exponential form

x^k=p-5

Change of Base

1

What is the change of base formula for log₄8.1?

(log8.1)/(log4)

2

Evaluate log₉3.87 (round your answer to the nearest thousandth).

0.616

3

Evaluate log₃(2/9) and round your answer to the nearest thousandth.

-2.170

4

What is the change of base formula for log₈104.561?

log104.561/log8

5

Evaluate log₆72.85 and round your answer to the nearest thousandth.

2.393

Condense or Expand

1

Condense 5log₃c + 10log₃x

log₃(c⁵x¹⁰)

2

Expand log₉(xy⁵)⁶

6log₉x + 30log₉y

3

Condense 16log₄a - 4log₄b

log₄(a¹⁶/b⁴)

4

Mrs. Megan will write this on the white board:

Expand log₇((cube root of x) times y⁵)

1/3log₇x + 5log₇y

5

Mrs. Megan will write this on the board:

Condense 1/2log₁₁x + 1/2log₁₁y - log₁₁z

Express all solutions in radical form.

log₁₁(sq.rt(xy)/z)

Solving Equations

1

Solve for x:

log2x + log5 = log (x+18)

x=2

2

Solve for x:

log₆(x+5) = 3

x = 211

3

Solve e^2x = 5.  Round your answer to the nearest thousandth.

x = 0.805

4

Solve ln5 + lnx = 2.  Round your answer to the nearest thousandth.

x = 1.478

5

Solve for x:

4 - 8log₇2x = -28

x = 2401/2 or 1200.5

Compound Interest

1

What is the formula for compound interest?

A=Pe^rt

2

Find the present value of $5000 to be received in 2 years if the money can be invested at 12% annual interest rate compounded continuously.

$6356.25

3

Pam Beesly invests some money at 2% compounded continuously. If after 6 years she has $1.691.25, what was her initial investment?

$1500

4

Bob Vance, of Vance Refrigeration, invests $3,500 continuously for 5 years.  At the end of the investment, Bob Vance, of Vance Refrigeration, has $3868.10. What was the interest rate?

2%

5

One thousand dollars is deposited in a savings account at 6% annual interest rate compounded continuously. How many years are required for the balance in the account to reach $2534.51?

15.5 years