Logarithms (Final Review)

Exponential Growth + Compound Interest

100

What is the exponential growth formula?

A=Pe^rt

200

Evaluate A=55(.89)^x for A if x=8

A=21.65

300

You deposit $1500 in an account that pays 5% interest compounded quarterly. How much money do you have after 6 years?

$2021.03

400

In 1995 there are 28,447,000 people. Growing exponentially at a rate of 1.1% per year, how many people will there be in 2004?

31,407,375 people

500

A mouse population is 25,000 and is increasing exponentially at a rate of 20%. How many years will it take for the mouse population to get to 100,000?

6.93 years

Exponential and log Functions

100

What is this: A(t) = P(1 + r/n)^nt

Compound interest formula

200

How much money would you have if you deposited $750 at 6.7% interest compounded quarterly for 13 years?

$1779.09

300

v = log₄( 64 ), solve for v

v=3

400

log_v( 9 ) = 1/2 Solve for v.

v=81

500

log₂₇( sqrt( 3 ) ) = ?

1/6

Common logs

100

If log_ax = log_by, then x=y. What property is this?

one-to-one correspondence property of logarithms

200

Write the follow as a sum or difference of logarithms. Then simplify, if possible--> log₂ 8xy

3 + log2( x ) + log2( y )

300

For any positive real numbers a=1, b=1 and x > 0 log_b( x ) = log( x ) / log( b ). What is this formula called?

Change of Base Formula

400

Solve. 6^x+2=21

x=-0.30

500

Solve for x: 12^x=7(5^x)

x=2.22

The Natural Base, e

100

What is the symbol that stands for 2.71828...

e

200

Solve for x: e^2x=9

x=1.10

300

Solve: lne³

3

400

e^x = 30, write an equivalent exponential or logarithm function.

What is ln(30) = x

500

Solve for x: lnx = ln(2x²) - 2

x=50

Solving log + exponential equations

100

How can you rewrite this equation 10logx?

logx¹⁰

200

Solve for x: 26^9x+5=1

x=-5/9

300

Solve for x: 4^x+2=14

x=-0.96

400

Solve for x: log₂(x+2)+log₂3=log₂27

x=7

500

Solve for x: log₄(x²-x)=log₄6

x=3 and x=-2