Properties of Logarithms

Expand #1

100

What are the three steps to follow when expanding a logarithm, in the correct order?

1. Division (Quotient Property)

2. Multiplication (Product Property)

3. Exponent (Power Property)

200

One logarithm multiplied can be rewritten as ___ using the ___ property?

Two logarithms added, product property

300

Expand log₈(2x/y)

log₈2 + log₈x - log₈y

400

Expand ln(x²/y³)

2lnx - 3lny

500

Expand ln(x³z/y)

3lnx + lnz - lny

Condense #1

100

What are the three steps to follow when condensing a logarithm, in the correct order?

1. Exponent (Power Property)

2. Multiplication (Product Property)

3. Division (Quotient Property)

200

Two logarithms subtracted can be rewritten as ___ using the ____ property?

One logarithm divided, quotient property

300

Condense log6 + log3 - log9

log((6*3)/9) = log2

400

Condense 3log₆x + 7log₆y

log₆(x³y⁷)

500

Condense ln3 + 4lnx - lny

ln(3x⁴/y)

Expand #2

100

Expand log₂(9/4)

log₂9 - log₂4

200

Expand log₃(5x)

log₃5 + log₃x

300

Expand log₇(y⁴)

4log₇(y)

400

Expand log(3x⁶/5)

log3 + 6logx - log5

500

Expand log₉(6x²/11y)

log₉6 + 2log₉x - log₉11 - log₉y

Condense #2

100

Condense log₂6 + log₂8

log₂(6*8) = log₂48

200

Condense log₃10 - log₃5

log₃(10/5) = log₃2

300

Condense 6lnx

lnx⁶

400

Condense lny + 4lnx - 9lnz

ln(yx⁴/z⁹)

500

DOUBLE JEOPARDY

Condense 2log₉x - log₉y - 3log₉z

hint: think about practice problem #4

log₉(x²/yz³)

Change of Base/Review

100

Evaluate log₆43 using common logarithms.

log43/log6 = 2.099

200

Evaluate log₄72 using natural logarithms.

ln72/ln4 = 3.085

300

Define what "a" does as a transformation, what value does it affect, and when graphing a logarithm with an "a" value what do you need to do?

Vertical stretch or compression (shrink), y-values, create a second table.

400

What do the variables represent in our interest formula A = P(1+(r/n))^nt?

A = Total amount

P = Principal or initial amount

r = rate (as a decimal)

n = number of times compounded within one year

t = time in years

500

DOUBLE JEOPARDY

Find the inverse of: y = 2log₃x + 5

y = 3^((x-5)/2)