Post Test: Exponential Expressions and Equations

Which logarithmic equation correctly rewrites this exponential equation? 8 ^x = 64

log (base) 8 of 64 = x A.

What is the solution to this equation? ln⁡(x+6)−ln⁡(2⁢x−1)=0

A. x = 7

What is the solution to this equation? 9^x - 1 = 2

c. 1/2

The sound level, β, in decibels (dB), of a sound with an intensity of I is calculated in relation to the threshold of human hearing, I0, by this equation. β=10⁢log⁡(II0) The threshold of human hearing is 10-12⁢watts/meter2. The sound level of a jet plane is approximately 140 dB. The intensity of the sound of a jet plane is approximately _______________ watts/meter2.

100

Cameron purchased an electric guitar for $1,875. The value of the guitar depreciates by 20% each year. In how many years will the guitar be valued at $768?

4 years

Type the correct answer in the box. log ⁡14/3 + log ⁡11/5 − log ⁡22/15 = log _____

7

Which expression is equivalent to the given expression? ln⁡(2e/x)

A. 1 + ln 2 - ln x

What is the approximate value of this logarithmic expression? log8⁡ 24

A. 1.53

What is the solution to this equation? 8(e) ^ (2⁢x+1) = 4

C. x = ( ln (.5) - 1 ) / 2

What is the solution set to this equation? log4 ⁡(x−3) + log4⁡ (x+3) = 2

C. x = -5 and x = 5

Which exponential equation is equivalent to this logarithmic equation? log⁡x=4

D. 10 ^ 4 = x

The maximum occupancy of a concert hall is 1,200 people. The hall is hosting a concert, and 175 people enter as soon as the doors open in the morning. The number of people coming into the hall then increases at a rate of 30% per hour. If t represents the number of hours since the doors open, which inequality can be used to determine the number of hours after which the amount of people in the concert hall will exceed the occupancy limit?

D. 175 (1.390) ^t > 1,200

What is the solution to this equation? log3⁡ (4⁢x) − 2 ⁢log3⁡ x = 2

D. 4/9

Which logarithmic equation is equivalent to this exponential equation? 2,400 = 7,500⁢(10) ^-x

D. x = -log (8/25)

What is the solution to this equation? log6⁡ x + log6⁡ 3 = log 6 ⁡(x+1)

D. x = 1/2

Which exponential equation is equivalent to this logarithmic equation? logx⁡ 5 + logx ⁡12 = 7

D. x^7 = 60

Paul is gathering data about moss growth in a local forest. He measured an area of 11 square centimeters on one particular tree and will come back in 6 months to measure the growth of the moss. If the area covered by moss multiplies by one and a half times each month, approximately how much area will the moss cover when Paul returns?

a. 125.3 cm^2

A new high school opens in a thriving suburban community. The number of students signed up to attend the school in its first year is 532, and the population of students is predicted to increase at a rate of 16% per year. Which inequality can the high school use to determine the number of years, t, until the student population is larger than 2,025?

b. 523 (1.16)^t > 2,025; 17 years