Exponents And Logarithms Quiz 2
Exponents and Logarithms
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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