Exponential Equations and Logarithmic Form

Solve the exponential equation 2^x = 8 using logarithms.

• x = 3

• x = 2

• x = 6

• x = 4

Convert the exponential equation 5^3 = 125 to logarithmic form.

• log5(3) = 125

• log3(125) = 5

• log125(5) = 3

• log5(125) = 3

A population of bacteria increases by 70% each hour. If there are initially 100 bacteria, how many will there be after 9 hours?

• 11859

• 12746

• 13956

• 14251

A radioactive substance decays by 20% each day. If there are initially 500 grams of the substance, how much will be left after 5 days?

• 163.84 grams

• 250.13 grams

• 75.24 grams

• 100 grams

Solve the exponential equation 3^(x) = 50 using logarithms.

• x = 2.41

• x = 3.11

• x = 3.56

• x = 3.91

Convert the exponential equation 6^4 = 1296 to logarithmic form.

• log1296(6) = 4

• 6log(1296) = 4

• log6(1296) = 4

• log4(1296) = 6

A population of rabbits increases by 20% every year. If there are initially 50 rabbits, make an equation to find the rabbit population.

• y=50*20^x

• y=20*50^x

• y=50*1.2^x

• y=50+1.20x

A radioactive substance decays by 10% each week. If there are initially 1000 grams of the substance, how much will be left after 4 weeks?

• 300 grams

• 500 grams

• 656.1 grams

• 800 grams

Solve the exponential equation 4^(x) = 100 using logarithms.

• x = 3.32

• x = 3.51

• x = 3.78

• x = 3.05

Convert the exponential equation 7^5 = 16807 to logarithmic form.

• log7(5) = 16807

• log16807(7) = 5

• log5(16807) = 7

• log7(16807) = 5