Mathematics Quiz

If logs (log4 1024) = x, what is the value of x?

• 1

• 2

• 3

Answer explanation

To find x in log4 1024, we need to determine what power we raise 4 to get 1024. Since 4^2 = 16 and 4^5 = 1024, we find that x = 5. Therefore, log4 1024 = 5, making the correct answer 2.

If logs(x + 1)² = logs(x² - 3), what is the value of x?

• -2

• -1

• 1

Answer explanation

To solve logs(x + 1)² = logs(x² - 3), we can set (x + 1)² = x² - 3. Expanding gives x² + 2x + 1 = x² - 3. Simplifying leads to 2x + 4 = 0, so x = -2. Thus, the correct answer is -2.

A city's population grows exponentially at an annual rate of 2%. If the current population is 100,000, what will the population be in 5 years?

• 106,120

• 108,242

• 110,409

• 112,416

Answer explanation

To find the population in 5 years, use the formula P = P0 * (1 + r)^t. Here, P0 = 100,000, r = 0.02, and t = 5. Calculating gives P = 100,000 * (1.02)^5 ≈ 108,242, which matches the correct answer.

A culture of 10 bacteria in a petri dish doubles every hour. How many bacteria will there be after 3 hours?

• 60

• 70

• 80

• 90

Answer explanation

The bacteria double every hour. Starting with 10, after 1 hour there are 20, after 2 hours 40, and after 3 hours 80. Therefore, the correct answer is 80.

Immanuel deposits P10,000 in a bank that pays 3% compound interest annually. How much money will he have after 2 years?

• Php10,160.00

• Php10,269.00

• Php10,409.00

• Php10,609.00

Answer explanation

To calculate the amount after 2 years with 3% compound interest, use the formula A = P(1 + r)^n. Here, A = 10000(1 + 0.03)^2 = 10000(1.0609) = Php10,409.00. Thus, the correct answer is Php10,409.00.

Suppose a culture of 200 bacteria are put in a petri dish and the culture doubles every hour. How many bacteria will there be after 3 hours?

• 400

• 800

• 1,600

Answer explanation

The bacteria double every hour. Starting with 200, after 1 hour there are 400, after 2 hours 800, and after 3 hours 1600. Therefore, after 3 hours, there will be 800 bacteria.

How do you express log3 4x² as a sum of simpler logarithms?

• log34 + 2log3 x

• log34 + log3 x

• 2 log34 + 2log 3 x

• 2log34 + log3 x

Answer explanation

To express log3(4x²), use the properties of logarithms: log3(ab) = log3 a + log3 b and log3(a^b) = b log3 a. Thus, log3(4x²) = log3 4 + log3(x²) = log3 4 + 2 log3 x, which matches the correct choice.

How do you evaluate log₂ 128 - log3 3 + log4 16?

• 5

• 6

• 7

Answer explanation

log₂ 128 = 7 (since 2^7 = 128), log₃ 3 = 1 (since 3^1 = 3), and log₄ 16 = 2 (since 4^2 = 16). Thus, log₂ 128 - log₃ 3 + log₄ 16 = 7 - 1 + 2 = 6. The correct answer is 6.

How do you express 3log x - 2log y as a single logarithm?

• log

• log x² + y²

• log x³y²

• log x³y²

Answer explanation

To combine 3log x - 2log y, use the properties of logarithms: 3log x = log x³ and -2log y = -log y². Thus, 3log x - 2log y = log x³ - log y² = log(x³/y²). The correct expression is log x³y².

What is the domain and range of y= log3(x + 2)?

• D = {x ER|x # 1} , R = R

• D = {x E Rx = -2}, R = R

• D = R, R = {y € Rly > 2}

• D= {x E Rx = 2}, R = R

Answer explanation

The function y = log3(x + 2) is defined for x + 2 > 0, so x > -2. Thus, the domain is D = {x ∈ R | x > -2}. The range is all real numbers R = R. The correct choice is not listed; the provided answer is incorrect.