1. Grade Distribution A B C D F 1st 4th 7th 9th 11 7 9 4 12 6 2 3 1
No Shows
100+
Range
65-100
59-95
71-103
64-96
Avg
86.27
84.8
87.7
80.62
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7.4a - Change of Base

2. Section 7.4A, Revised ©2013, vdang@houstonisd.org
Change of Base
Section 7.4A, Revised ©2013,
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7.4a - Change of Base

3. We’ll answer that question later…
Review
Review: What’s 23 and 24 = ?
Answer: 8 and 16 because its 2 · 2 · 2 = 8 and 2 · 2 · 2 · 2 = 16.
So we know that 23 = 8 and 24 = 16.
However, what is 2x = 10?
We’ll answer that question later…
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7.4a - Change of Base

4. Change of Base Change of Base Formula:
We use this formula when we need to solve for x
Remember the question, 2x = 10?
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7.4a - Change of Base

5. Change of Base
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7.4a - Change of Base

6. We will need to use calculators to figure this out.
Example 1
Solve for x, 2x = 10
Put it in this equation:
We will need to use calculators to figure this out.
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7.4a - Change of Base

7. Example 1 Given 2x = 10, solve for x Put it in this equation:
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7.4a - Change of Base

8. Example 2 Evaluate log26 Put it in this equation: 2/27/2019 12:23 PM
7.4a - Change of Base

9. Example 3
Evaluate
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7.4a - Change of Base

10. Your Turn
Evaluate
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7.4a - Change of Base

11. Example 4 Simplify log552+x without a calculator 2/27/2019 12:23 PM
7.4a - Change of Base

12. Example 5 Evaluate 3logx4.52 = 4.52 2/27/2019 12:23 PM
7.4a - Change of Base

13. Your Turn Evaluate 2.5log2.519 without a calculator 2/27/2019 12:23 PM
7.4a - Change of Base

14. Example 6
Evaluate log010
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7.4a - Change of Base

15. Example 7
The population of a coastal town currently holds 3,400 and grows at a rate of 3% per year. The growth can be expressed by the exponential equation P = 3400( )t, where P is the population after t years. Find the number of years it will take for the population to have at least 5,000 people. Round answer to the 3 decimal places.
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7.4a - Change of Base

16. Your Turn
The population of Wahoo, Nebraska is declining at a rate of 7% per year. The decline can be expressed by the exponential equation P = C(1 – 0.07)t where P is the population after t years and C is the current population. If the population was 8,500 in 2004, when will the population be less than 6,000? Round answer to the nearest whole number
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7.4a - Change of Base

17. Assignment
Worksheet
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7.4a - Change of Base