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:log

_{5}(x - 20) + log_{5}(x) = 3Explanation

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) = log

_{3}(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 = log

_{b}(2) and q = log_{b}(7), write in terms of p and q.log_{b}(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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