Exponents And Logarithms Quiz 2
Exponents and Logarithms Quiz 2 assesses understanding of key mathematical concepts including simplification, acidity comparison using pH, compound interest calculations, and logarithmic functions. This quiz is essential for learners aiming to enhance their proficiency in advanced math topics.
Questions and Answers
- 1.
Explanation
16^x = 8^(-1/4)
2^4x = 2^(-3/4)
4x = -3/4
x = -3/16Rate this question:
- 2.
Simplify:
- 3.
Simplify:
- 4.
How much more acidic is a substance that has a pH reading of 2 than one that has a pH reading of 7?
Explanation
A substance with a pH reading of 2 is 100,000 times more acidic than a substance with a pH reading of 7. The pH scale is logarithmic, meaning that each unit represents a tenfold difference in acidity or alkalinity. Therefore, the difference between a pH of 2 and 7 is 5 units, which corresponds to a difference of 10^5 or 100,000 times in acidity.Rate this question:
- 5.
Approximately how many years will it take you to double your money if you invest it in an account that compounds monthly at an interest rate of 3%?
Explanation
If you invest your money in an account that compounds monthly at an interest rate of 3%, it will take approximately 23 years to double your money.Rate this question:
- 6.
Solve:log5(x - 20) + log5(x) = 3
Explanation
log5(x^2-20x)=3
5^3=x^2-20x
x^2-20x-125=0
(x-25)(x+5) = 0
x = 25 works, x = -5 is not in domainRate this question:
- 7.
What is the domain of the graph y = log(x + 4)?
Explanation
The vertical asymptote shifted left four units --> x = -4 and the graph is to the right of this asymptote.Rate this question:
- 8.
What is the inverse function of f(x) = log3(x)?Write the equation as y = __________
Explanation
The inverse function of f(x) = log3(x) can be found by interchanging x and y and solving for y. By doing so, we get y = 3^x, which is the same as the given answer. This equation represents the inverse function of f(x) = log3(x), where y is the exponent to which 3 must be raised to obtain x.Rate this question:
- 9.
What is inverse of the function y = 10^x?Write as y = ___________
Explanation
The inverse of a function undoes the original function. In this case, the original function is y = 10^x, which represents exponential growth. The inverse function, y = logx, represents logarithmic growth, where x is the base and y is the exponent. Therefore, the correct answer is y = logx.Rate this question:
- 10.
Expand:
Explanation
The given expression can be simplified using logarithmic properties. We can rewrite the expression as log(x^(1/2)) - log(3) - log(y^2). Using the power rule of logarithms, we can simplify further to log(sqrt(x)) - log(3) - log(y^2). Finally, using the quotient rule of logarithms, we can combine the terms to get log((sqrt(x))/(3y^2)). Therefore, the answer is 1/2log(x) - log(3) - 2log(y).Rate this question:
- 11.
If p = logb(2) and q = logb(7), write in terms of p and q.logb(49/8)
Explanation
The given expression is logb(49/8). We can rewrite 49/8 as (7^2)/(2^3) using the properties of logarithms. Then, we can use the property logb(x/y) = logb(x) - logb(y) to simplify the expression. Therefore, logb(49/8) becomes logb(7^2) - logb(2^3), which is equal to 2q - 3p. Thus, the correct answer is 2q - 3p.Rate this question:
- 12.
Solve: log18 - logx = logx - log2
Explanation
log(18/x) = log(x/2)
36 = x^2
x = pos 6 only (x > 0 is domain)Rate this question:
- 13.
Solve:1/3(lnx) = 4
Explanation
ln(x^(1/3)) = 4
e^4 = x^(1/3)
e^12 = xRate this question:
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Mar 20, 2023Quiz Edited by
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Feb 14, 2011Quiz Created by
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