Pre Calc Checkup 4

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Date:
Graded Assignment
Checkup: Introduction to Logarithms
Answer the following questions using what you've learned from this lesson. Write your responses in the space provided, and turn the assignment in to your instructor.

1. Write the equation y = bx in logarithmic form.

logb y

2. Write the equation y = ex in logarithmic form.

loge y

3. Write the equation y = log x in exponential form.
X = 1y

4. Write the equation y = ln x in exponential form.

X = loglny

5. Show two ways of finding y if y = log4 64. Explain your thinking.

1. 4? = 64 (4 x 4 = 16 x 4 = 64) 43 = 64 Exponent equals 3

2. log64 = 1.8 = 3 log4 .60

log4 64 is equivalent to log64 log4

6. Find y if y = log32 1. Explain your thinking.

Y = approx. 1.5

If I used my calculator for log32 and then multiply it by 1, I get 1.5.

7. Use the rules of logarithms to expand .

logb (x+3)4 + logb (x-5)7

8. Use the rules of logarithms to expand .

logb a3b5 – logb c8

9. Write the expression as a single logarithm.

log (x – 2)3 (x + 2) x2 - 4

10. Write the expression 5ln M + 3ln N – 2ln P – ln R as a single logarithm.

ln (M)5 + ln (N)3 – ln (P)2 – ln (R)

ln (M)5 + (N)3 – (P)2 R

11. Solve for x if 5 = log3 (x2 + 18).

X = +/- i√18 – 5ln(10) ln(3)

12. Solve for x if -2 = log(3x + 5).

X = -499/300

13. Use the change-of-base formula and a calculator to evaluate log5 65 to two decimal places.

Log65 = 1.8 = 2.61
Log5 .69

14. Use the change-of-base formula and a calculator to evaluate log8 125 to two decimal places.

Log125/log8 = 2.1/.90 = 2.33

15. How much more intense is an earthquake that measures 7.5 on the Richter scale than one that measures 6.2? (Recall that the Richter scale defines magnitude of an earthquake with the