Name
Algebra 2 Section 7.1-7.4 STUDY GUIDE
1. Tell whether the function shows growth or decay.
a.
f(x) = 100(1.05)x
b.
7 𝑥
g(x) = 5 (8)
2. In 1626, the Dutch bought Manhattan Island, now part of New York City, for $24 worth
of merchandise. Suppose that, instead, $24 had been invested in an account that paid
3.5% interest each year. Find the balance in 2008.
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3. Write the inverse of 𝑓(𝑥) = 4 𝑥 + 6
4. Write the inverse of 𝑓(𝑥) = −4𝑥 − 7.
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5. A thermometer gives a reading of 8oC. Use the formula 𝐶 = 9 (𝐹 − 32). Write the
inverse function and use it to find the equivalent temperature in oF.
6. What is the exponential form of 𝑙𝑜𝑔2 144 = 2?
7. What is the logarithmic form of 33 = 27?
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8. Evaluate 𝑙𝑜𝑔5 5.
9. Evaluate 𝑙𝑜𝑔2 128.
10. Evaluate 𝑙𝑜𝑔8 1.
11. Solve 𝑙𝑜𝑔2 𝑥 = −4.
12. Solve 𝑙𝑜𝑔𝑥 81 = 4.
13. Solve 𝑙𝑜𝑔5 100 − 𝑙𝑜𝑔5 𝑥 = 𝑙𝑜𝑔5 25.
14. Solve 𝑙𝑜𝑔6 36 = 𝑙𝑜𝑔6 3 + 𝑙𝑜𝑔6 12.
15. Simplify COMPLETELY
𝑙𝑜𝑔2 80 − 𝑙𝑜𝑔2 10 =
16. Simplify COMPLETELY
𝑙𝑜𝑔6 8 + 𝑙𝑜𝑔6 27 =
17. Evaluate by changing to Base 10
𝑙𝑜𝑔3 30 =
18. Evaluate by changing to Base 10
𝑙𝑜𝑔32 8 =
19. Simplify the expression (think Inverse Properties)
𝑙𝑜𝑔8 83𝑥+1 =
20. Simplify the expression (think Inverse Properties)
2𝑙𝑜𝑔2 27 =