Packet C Homework #2 1.

Name:_____________________________________________________________

Solve for x using the properties of logarithms. Show your work. a. log 4 𝑥 + log 4 3 = log 4 (𝑥 + 2)

b. log 3 𝑥 = log 3 5 + 1

c. log 5 8𝑥 − log 5 2 = log 5 36

d. log 6 (3𝑥 + 7) = log 6 2 + log 6 (𝑥 − 5)

e. log10 𝑥 + log10 (𝑥 + 3) = log10 10

f. log10 (𝑥 − 4) + log10 (𝑥 + 1) = log10 (𝑥 − 8)

2.

Recall that log 2 2 means the time it takes for the duckweed to grow to 2 m2 when doubling. We can write log 2 2 = 1 because it would take one day. a. log 3 3 =

log 4 4 =

log 5 5 =

log 6 6 =

b. log 3 9 =

log 4 16 =

log 5 25 =

log 6 36 =

c. log 3 27 =

log 4 64 =

log 5 125 =

log 6 216 =

3. Use the properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. a. log 5 (7 ∙ 3)

b. log 7 (7𝑥)

c. log 𝑏 𝑥 3

𝑒2

7

64

d. log 7 ( ) 𝑥

e. ln ( ) 5

f. log 4 ( ) 𝑦

g. ln√𝑥

h. log 𝑏 (𝑥 2 𝑦)

i. log 4 ( ) 64

36

j. log 6 (

√

) 𝑥+1

𝑥2𝑦

l. log 𝑏 (

) 𝑧2

k. ln [

𝑥 3 √𝑥 2 +1 (𝑥+1)4

m. log [

√𝑥

]

10𝑥 2 √1−𝑥 7(𝑥+1)2

]

4. Use the properties of logarithms to condense each logarithmic expression. Where possible, evaluate logarithmic expressions without using a calculator. a. log5 + log2

b. ln x + ln 7

c. log 2 96 − log 2 3

d. log 2 (2𝑥 + 5) − log 2 𝑥

e. log x + 3log y

f.

g. 2 log 𝑏 𝑥 + 3 log 𝑏 𝑦

h. 5 ln 𝑥 − 2 ln 𝑦

i. 3 ln 𝑥 − ln 𝑦

j. 4 ln(𝑥 + 6) − 3 ln 𝑥

k. 3 ln 𝑥 + 5 ln 𝑦 − 6 ln 𝑧

l. (log 𝑥 + log 𝑦)

1

m. 2 ln 𝑥 − ln 𝑦 2

1 2

ln 𝑥 + ln 𝑦 1 3

1 2

n. log 𝑥 + log(𝑥 2 − 1) − log 7 − log(𝑥 + 1)