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Question 1: (1 point) Evaluate log3127‾‾‾√4without...

Question 1: (1 point)

Evaluate log3127‾‾‾√4without using a calculator.

If the answer is not an integer, enter it as a fraction in simplest form.

log3127‾‾‾√4 = __________

Question 2: (1 point)

Evaluate log162+log163−log16393,216without using a calculator.

log162+log163−log16393,216= __________

Question 3: (1 point)

Use the properties of logarithms to expand the expression.

log22+x32x‾‾‾‾‾√6

(a)

16log2(2+x)−5−log2x

(b)

16log2(2+x)−56+16log2x

(c)

16log2(2+x)−56−16log2x

(d)

116log2(x)−5−log2x

Question 4: (1 point)

Use the properties of logarithms to expand the expression.

ln7+xx4‾‾‾‾‾√5

(a)

15ln(7+x)+45lnx

(b)

15ln(7+x)−4lnx

(c)

15ln(7)+15lnx

(d)

15ln(7+x)−45lnx

Question 5: (1 point)

Use the properties of logarithms to write the expression as a single logarithm, if possible.

3logb4x3−13logb(4x+9)

(a)

logb(64x9(4x+9)3)

(b)

logb⎛⎝⎜⎜64x3(4x+9)‾‾‾‾‾‾‾√3⎞⎠⎟⎟

(c)

logb⎛⎝⎜⎜64x9(4x+9)‾‾‾‾‾‾‾√3⎞⎠⎟⎟

(d)

logb(64x9(4x+9)‾‾‾‾‾‾‾‾√3)

(e)

logb⎛⎝⎜⎜4x9(4x+9)‾‾‾‾‾‾‾√3⎞⎠⎟⎟

Question 6: (1 point)

Use the Change of Base Formula and common logs or natural logs to approximate the value of log8(78)using a calculator.

If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.

log8(78)= ____________

Question 7: (1 point)

Solve.

1729=2434t−5

If the answer is not an integer, enter it as a fraction.

t=____________

Question 8: (1 point)

Solve.

64x+5=(132,768)1−x

If the answer is not an integer, enter it as a fraction.

x=____________

Question 9: (1 point)

Solve.

3(10x)−3=21

If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.

x=____________

Question 10: (1 point)

Solve.

(34)x−61−x=0

If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.

x= ____________

Question 11: (1 point)

Solve.

5+5e4−x5+1=12

If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.

x= ____________

Question 12: (1 point)

Solve.

9+9e10x−4=11

If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.

x= ____________

Question 13: (1 point)

Solve.

ln(x+4)7+10=52

If the answer is not an integer, enter it as a decimal. Round to the nearest hundredth, if needed.

x= ____________

Question 14: (1 point)

Solve.

−8=6−log8(4−x)7

If the answer is not an integer, enter it as a decimal. Round to the nearest hundredth, if needed.

x= ____________

Question 15: (1 point)

Use the Distance Modulus Formula, M=5logr−5(where Mis the distance modulus and ris the distance from Earth to a star in parsecs), and the fact that 1parsec is approximately 3.3light years, to ﬁnd the distance in light years from Earth to a star with distance modulus 0.66.

If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.

____________light years

Question 16: (1 point)

Find the half-life to the nearest tenth of a year of a radioactive substance that decays from 75mg to 18.75mg in 23years according to the exponential decay model y=ae−bxwhere ais the initial amount and yis the amount remaining after xyears.

HINT: Find the b-value, then use this value to write the exponential decay model for this substance with initial amount 75mg.

If the answer is not an integer, round to the nearest tenth of a year, if needed.

half-life ≈ ____________years

Question 17: (1 point)

An investor wants to analyze the earnings of a mutual fund account. Three years ago, the value of the account was $17,000and it is now worth $21,250(no additional deposits were made). If the account is compared to a bank account paying interest that is compounded continuously, what interest rate would the bank account have to pay to match the mutual fund accounts earnings?

Round the answer to the nearest hundredth of a percent.

Interest Rate ≈ ____________%

Evaluate log3127‾‾‾√4without using a calculator.

If the answer is not an integer, enter it as a fraction in simplest form.

log3127‾‾‾√4 = __________

Question 2: (1 point)

Evaluate log162+log163−log16393,216without using a calculator.

log162+log163−log16393,216= __________

Question 3: (1 point)

Use the properties of logarithms to expand the expression.

log22+x32x‾‾‾‾‾√6

(a)

16log2(2+x)−5−log2x

(b)

16log2(2+x)−56+16log2x

(c)

16log2(2+x)−56−16log2x

(d)

116log2(x)−5−log2x

Question 4: (1 point)

Use the properties of logarithms to expand the expression.

ln7+xx4‾‾‾‾‾√5

(a)

15ln(7+x)+45lnx

(b)

15ln(7+x)−4lnx

(c)

15ln(7)+15lnx

(d)

15ln(7+x)−45lnx

Question 5: (1 point)

Use the properties of logarithms to write the expression as a single logarithm, if possible.

3logb4x3−13logb(4x+9)

(a)

logb(64x9(4x+9)3)

(b)

logb⎛⎝⎜⎜64x3(4x+9)‾‾‾‾‾‾‾√3⎞⎠⎟⎟

(c)

logb⎛⎝⎜⎜64x9(4x+9)‾‾‾‾‾‾‾√3⎞⎠⎟⎟

(d)

logb(64x9(4x+9)‾‾‾‾‾‾‾‾√3)

(e)

logb⎛⎝⎜⎜4x9(4x+9)‾‾‾‾‾‾‾√3⎞⎠⎟⎟

Question 6: (1 point)

Use the Change of Base Formula and common logs or natural logs to approximate the value of log8(78)using a calculator.

If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.

log8(78)= ____________

Question 7: (1 point)

Solve.

1729=2434t−5

If the answer is not an integer, enter it as a fraction.

t=____________

Question 8: (1 point)

Solve.

64x+5=(132,768)1−x

If the answer is not an integer, enter it as a fraction.

x=____________

Question 9: (1 point)

Solve.

3(10x)−3=21

If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.

x=____________

Question 10: (1 point)

Solve.

(34)x−61−x=0

If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.

x= ____________

Question 11: (1 point)

Solve.

5+5e4−x5+1=12

If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.

x= ____________

Question 12: (1 point)

Solve.

9+9e10x−4=11

If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.

x= ____________

Question 13: (1 point)

Solve.

ln(x+4)7+10=52

If the answer is not an integer, enter it as a decimal. Round to the nearest hundredth, if needed.

x= ____________

Question 14: (1 point)

Solve.

−8=6−log8(4−x)7

If the answer is not an integer, enter it as a decimal. Round to the nearest hundredth, if needed.

x= ____________

Question 15: (1 point)

Use the Distance Modulus Formula, M=5logr−5(where Mis the distance modulus and ris the distance from Earth to a star in parsecs), and the fact that 1parsec is approximately 3.3light years, to ﬁnd the distance in light years from Earth to a star with distance modulus 0.66.

If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed.

____________light years

Question 16: (1 point)

Find the half-life to the nearest tenth of a year of a radioactive substance that decays from 75mg to 18.75mg in 23years according to the exponential decay model y=ae−bxwhere ais the initial amount and yis the amount remaining after xyears.

HINT: Find the b-value, then use this value to write the exponential decay model for this substance with initial amount 75mg.

If the answer is not an integer, round to the nearest tenth of a year, if needed.

half-life ≈ ____________years

Question 17: (1 point)

An investor wants to analyze the earnings of a mutual fund account. Three years ago, the value of the account was $17,000and it is now worth $21,250(no additional deposits were made). If the account is compared to a bank account paying interest that is compounded continuously, what interest rate would the bank account have to pay to match the mutual fund accounts earnings?

Round the answer to the nearest hundredth of a percent.

Interest Rate ≈ ____________%

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