Exponentials And Logarithms

Evaluate the Log

Convert To An Exponential

Convert To A Logarithm

Compound Interest

Solving Logs and Exponentials

100

Evaluate:

Log_2 16

100

Convert to an exponential equation.

log_2 32=5

2^5=32

100

Convert to a Logarithm of form

2^3=8

log_2 8=3

100

What is the formula for annual compound interest? What does each variable represent?

A = P(1+r)^t

^{P Initial Investment}
^{r rate as a decimal}
^{t number of years}

100

Solve

4.5^x= 100

x = 3.062

200

Evaluate:

log_27 3

1/3

200

Convert to an exponential equation.

log_2 x=y

x=2^y

200

Convert to a Logarithm of form

12^3=1728

log_12 1728=3

200

What is the formula for compound interest for compounding more than once a year? What does each variable represent?

A = P(1+r/n)^nt

^{P Initial Investment}
^{r rate as a decimal}
^{t number of years}
^{n number of times compounded each year}

200

log₉(4x) = 2

x = 20.25

300

Evaluate:

log_4 1

300

Convert to an exponential equation.

log 1=0

10 ⁰= 1

300

Convert to a Logarithm of form

3^0=1

log_3 1=0

300

What is the formula for compound interest for compounding continuously? What does each variable represent?

A = Pe^rt

^{P Initial Investment}
^{r rate as a decimal}
^{t number of years}
^{e = 2.71828..}

300

log₃(x+2) = 4

x = 79

400

Evaluate:

log_5 (1/25)

-2

400

Convert to an exponential equation.

log_2 (x+3)=8

2^8=x+3

400

Convert to a Logarithm of form

10^(x+2)=29

log 29=x+2

400

A man invests $5,000 in an account that pays 8.5% interest per year, compounded quarterly. How much is in the account after 3 years?

$6435.09

400

3^x+4+ 1 = 13

x = -1.738

500

Evaluate:

log_2 (1/4)

-2

500

Convert to an exponential equation.

log_7 4=x-6

7^(x-6)=4

500

Convert to a Logarithm of form

5^3=x-3

log_5 (x-3)=3

500

A woman invests $6,500 in an account that pays 6% interest per year, compounded continuously. How much is in the account after 2 years?

$7328.73

500

10(4)^-x- 11 = 149

x = - 2