Logarithms

Convert

100

Write the exponential equation in logarithmic form.

6³ = 216

log₆216 = 

3

200

Write the logarithmic equation in exponential form. 

log100 = 2

10² = 

100

300

Write the logarithmic equation in exponential form. 

log (1/1000) = -3

10^? = (1/1000)

-3

400

Write the exponential equation in logarithmic form. 

64 = 4³

log₄64 = 3

500

Write the logarithmic equation in exponential form.

log₅5 = 1

5¹ = 5

Evaluate

100

Evaluate. Write your answer as a whole number, proper fraction, or improper fraction in simplest form.

log₅25 = 

2

200

Evaluate. Write your answer as a whole number, proper fraction, or improper fraction in simplest form. 

log1000 = 

3

300

Evaluate. Write your answer as a whole number, proper fraction, or improper fraction in simplest form. 

log₇(1/49) = 

-2

400

Evaluate. Write your answer as a whole number, proper fraction, or improper fraction in simplest form. 

log_(1/8)8 = 

-1

500

Evaluate. Write your answer as a whole number, proper fraction, or improper fraction in simplest form. 

log₈2 = 

1/3

Change of Base

100

Rewrite as a quotient of two common logarithms. Write your answer in simplest form.

log₆14 =

log14 / log6

200

Rewrite as a quotient of two common logarithms. Write your answer in simplest form. 

log₅19 =

log19 / log5

300

Rewrite as a quotient of two natural logarithms. Write your answer in simplest form. 

log₇6 =

(ln 6) / ln 7)

400

Rewrite as a quotient of two common logarithms. Write your answer in simplest form. 

ln 22 = 

log22 / log e

500

Rewrite as a quotient of two natural logarithms. Write your answer in simplest form. 

log₇11 = 

ln 11 / ln 7

Expand

100

Expand the logarithm. 

log₆xy

log₆x + log₆y

200

Expand the logarithm.

ln 5u = 

ln 5 + ln u

300

Expand the logarithm.

log (7/vu)

log 7 - (log v + log u)

or

log 7 - log v - log u

400

Expand the logarithm.

log(19u/tv)

log19 + log u - log t - log v

500

Can you prove this statement using properties of logarithms? 

log₆3 + log₆4 + log₆4 = log₆48 ?

yes

Compress

100

Compress the logarithmic expression.

log 7 + log z

log 7z

200

Compress the logarithmic expression.

log 7 - log y

log (7/y)

300

Compress the logarithmic expression.

log₂3 - 2log₂6 = 

log₂(1/12)

400

Compress the logarithmic expression.

ln u + 3ln t - ln v

ln (ut³/v)

500

Can you prove this statement using properties of logarithms? 

log9 + log4 + log2 = log26 ?

no