Logarithms are the inverse of exponentials

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Reference no: EM131753708

1. Exponential functions often involve the rate of increase or decrease of something such as a population, for example. If there is a population increase, it is a _______ function and when there is a decrease, it is a ________ function.

2. Write Eulers Number (e) to three decimal places.

3. A general formula for exponential Growth can be given by:

A = P ekt

In your textbook, or using another reliable source, research what values, P, A, k and t represent and write your answer. (Hint: What do each of the variables stand for?)

4. pH is a measure of the hydrogen ion concentration of a solution. It is defined as the negative logarithm of the hydrogen ion concentration. The equation is:

pH = - log [H+]

If an acid has an H+ concentration of 10-4, what's the pH?

5. The given x-value is a solution (or an approximate solution) of the equation.

42x-7 = 16

x = 5

True

False

6. Write the exponential equation in logarithmic form.

43 = 64

7. Use the One-to-One property to solve the equation for x.

e(3x+5) = e6

8. The exponential equation y=bx is equivalent to the logarithmic equation x=logby

True

False

9. Evaluate the function at the indicated value of x. Round your result to three decimal places.

f(x) = 500e(.05)x Value: x=2

10. Select the graph of the function. Indicate which graph is correct: 1st, 2nd, 3rd, or 4th

f(x) = 5x-1

11. Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. Assume all variables are positive.

log3 9x

12. The Logarithm Quotient Rule states:

logb(x / y) = logb(x) + logb(y)

logb(x / y) = logb(x) - logb(y)

logb(x y) = y · logb(x)

logb(c) = 1 / logc(b)

13. Logarithms are the inverse of exponentials.

True

False

Reference no: EM131753708

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