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 2/27/2019 12:23 PM 7.4a - Change of Base

Section 7.4A, Revised ©2013, vdang@houstonisd.org Change of Base Section 7.4A, Revised ©2013, vdang@houstonisd.org 2/27/2019 12:23 PM 7.4a - Change of Base

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… 2/27/2019 12:23 PM 7.4a - Change of Base

Change of Base Change of Base Formula: We use this formula when we need to solve for x Remember the question, 2x = 10? 2/27/2019 12:23 PM 7.4a - Change of Base

Change of Base 2/27/2019 12:23 PM 7.4a - Change of Base

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. 2/27/2019 12:23 PM 7.4a - Change of Base

Example 1 Given 2x = 10, solve for x Put it in this equation: 2/27/2019 12:23 PM 7.4a - Change of Base

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

Example 3 Evaluate 2/27/2019 12:23 PM 7.4a - Change of Base

Your Turn Evaluate 2/27/2019 12:23 PM 7.4a - Change of Base

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

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

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

Example 6 Evaluate log010 2/27/2019 12:23 PM 7.4a - Change of Base

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(1 + 0.03)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. 2/27/2019 12:23 PM 7.4a - Change of Base

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 2/27/2019 12:23 PM 7.4a - Change of Base

Assignment Worksheet 2/27/2019 12:23 PM 7.4a - Change of Base