Page 353 1) $1469.33 $1485.95 $1489.85 $1491.37 2) $7424.87 $7852.37 $7894.05 3) $585.83 4) $609.03 5) $610.40 6) $614.87 7) $639.76 8) $651.93 9) $563.75 10) $709.53 11) $582.02 1) {8} 2) {-5} 3) {11/3} 4) {-5/3} 5) {-2} 6) DNE 13) $3325.29 15) $3359.59 17) $6351.16 19) $568.59 21) Fund C 23) $385.18 4/20/2019 8:41 AM 5.4 - Common Logarithms

4/20/2019 8:41 AM 5.4 - Common Logarithms

Logarithmic Functions Section 5.4 Pre-Calculus AB PreAP, Revised ©2015 viet.dang@humble.k12.tx.us 4/20/2019 8:41 AM 5.4 - Common Logarithms

Real-Life Situation The pH scale is used in chemistry to determine the acidity or alkalinity of a solution. The scale ranges from 1 to 14, with 1 being the most acidic and 14 the most alkaline The difference in strength of an acid of pH 1 and that of pH 2 is not twofold, but tenfold The pH scale is actually a logarithm in the form: log10, thus, pH 1 = log1010, and pH 2 = log10100 4/20/2019 8:41 AM 5.4 - Common Logarithms

Real Life Situation The Richter scale is used to determine the strength of the ground movement. The larger the number, the more violent the movement Similar to the pH scale, an earthquake of magnitude 7 on the scale is ten times stronger than an earthquake of magnitude 6. Again, this is because the Richter scale is actually a logarithm: log10[measurement of movement of the earth] 4/20/2019 8:41 AM 5.4 - Common Logarithms

Real-Life Situation The Modified Richter Scale uses a modified scale. It is not ten-fold A separate equation is used Music “Semitones” The interval between two notes in semitones is the base-21/12 logarithm of the frequency ratio (or equivalently, 12 times the base-2 logarithm). Astronomy The magnitude measures the stars’ brightness logarithmically with vision Source: Wikipedia 4/20/2019 8:41 AM 5.4 - Common Logarithms

Key Terms Logarithms are defined as the INVERSE of an exponential function. It can be used specifically to find base powers. They are 10-fold. Exponential form: bx = a; where b is the BASE, x is the POWER, and a is the value. Logarithmic form: logba = x; b is the BASE, a is the ARGUMENT, and x is the value. It is read as “log of a base b” or “log base b of a” If the base is not given (such as log 3) it is understood to be COMMON BASE OF 10. 4/20/2019 8:41 AM 5.4 - Common Logarithms

Definition Logarithms are defined as the INVERSE of an exponential function. It can be used specifically to find base powers. They are 10-fold. If there is not a base given, the base is ALWAYS 10. 4/20/2019 8:41 AM 5.4 - Common Logarithms

Review What is the inverse function of y = 2x? 4/20/2019 8:41 AM 5.4 - Common Logarithms

To Identify Logarithms b = Base x = Power/Argument a = Value 4/20/2019 8:41 AM 5.4 - Common Logarithms

The Snail 4/20/2019 8:41 AM 5.4 - Common Logarithms

Example 1 Given 24 = 16, write this problem in logarithmic form Identify the components of this problem EXPONENT ARGUMENT BASE 4/20/2019 8:41 AM 5.4 - Common Logarithms

= Example 1 Given 24 = 16, write this problem in logarithmic form 5.4 - Common Logarithms

Example 2 Given 43/2 = 8, write this problem in logarithmic form 5.4 - Common Logarithms

Example 3 Given log4(1/16) = –2, write this problem in exponential form Identify the components of this problem ARGUMENT EXPONENT BASE 4/20/2019 8:41 AM 5.4 - Common Logarithms

Example 3 Given log4(1/16) = –2, write this problem in exponential form = 4/20/2019 8:41 AM 5.4 - Common Logarithms

Your Turn Given 10–2 = 1/100, write this problem in logarithmic form 4/20/2019 8:41 AM 5.4 - Common Logarithms

Example 4 Given log7(1/49) = x, write this problem in exponential form and solve for x (without a calculator) 4/20/2019 8:41 AM 5.4 - Common Logarithms

Your Turn Given log64(x) = 1/2, write this problem in exponential form and solve for x (without any calculator) 4/20/2019 8:41 AM 5.4 - Common Logarithms

Example 5 Given log279 = x, write this problem in exponential form and solve for x (without a calculator) 4/20/2019 8:41 AM 5.4 - Common Logarithms

Example 6 Given log832 = x, write this problem in exponential form and solve for x (without a calculator) 4/20/2019 8:41 AM 5.4 - Common Logarithms

Your Turn Given log 𝟖 𝟖 , write this problem in exponential form and solve (without a calculator) 4/20/2019 8:41 AM 5.4 - Common Logarithms

Example 7 Given log 100 = x, write this problem in exponential form and solve for x If there isn’t a base given, assume the base to be… 4/20/2019 8:41 AM 5.4 - Common Logarithms

Your Turn Given log 1/1000 = x, write this problem in exponential form and solve for x 4/20/2019 8:41 AM 5.4 - Common Logarithms

Assignment Worksheet 4/20/2019 8:41 AM 5.4 - Common Logarithms