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Today’s Date: 3/25/11 10.6 Applications of Logarithms
Antilog (Base 10) If log y = x then y is antilog of x y = antilog x y = 10 x Common log = base 10 log 6 = log 10 6 Write → Example 1) log y = 3.7135 y = antilog 3.7135 y = 10 3.7135 = 5170
Change-of-Base Formula base down low use your calculator base 10 Example 2) log button on your calculator is base 10
Change-of-Base Formula base down low Write in log form Example 2b)
T.O.O. #1 – 9 do the same way
Solve each equation using Change-of-Base Formula a) a) Calculation-ready form b) Solution to 3 significant digits b) a) b) or #11-13, 17, 19, 23 do same way
Solve each equation using Change-of-Base Formula a) a) Calculation-ready form b) Solution to 3 significant digits b) #15, 16, 22 Do same way
Solve each equation using Change-of-Base Formula a) Calculation-ready form b) Solution to 3 significant digits Take log of both sides Don’t forget ( ) Distribute Get terms with x on same side of =
Solve each equation using Change-of-Base Formula a) a) Calculation-ready form b) Solution to 3 significant digits b) Factor out x or Solve for x Put in calc with ( ) around denom ( )
Homework #1012 Finish 10.6 Worksheet #20, 21, 25 use change of base & #25 THINK!
10.14 Applications of Logarithms. Ex 1) Solve log x = Round to 4 decimal places Remember: Common log = base 10 log 6 = log 10 6 x =
Evaluating Logs and Antilogs Warm-up Solve: Learning Objective: to evaluate and solve equations with logs of bases other than those we’re used to.
C2: Solving Equations with Logarithms Learning Objective: to be able to solve equations of the form a x = b.
Pre-calc w-up 4/ Write the equation log e 13.7 = x in exponential form 2. Write the equation (1/4) -4 = 256 in log form 3. Evaluate the expression.
WARM - UP. SOLVING EXPONENTIAL & LOGARITHMIC FUNCTIONS SECTION 3.4.
Warm up. Solution Why do we care? Logarithms are functions that used to be very helpful, but most of their value has become obsolete now that we have.
Solving Equations with Logs Day 2. Solving equations with only one logarithm in it: If it is not base 10 and you can’t use your calculator, then the only.
Exponentials without Same Base and Change Base Rule.
Property of Logarithms If x > 0, y > 0, a > 0, and a ≠ 1, then x = y if and only if log a x = log a y.
Turn in your Quiz!!! Complete the following:. Section 11-5: Common Logarithms The questions are… What is a common log? How do I evaluate common logs?
C2: Change of Base of Logarithms Learning Objective: to understand that the base of a logarithm may need changing to be able to solve an equation.
Common Logarithms - Definition Example – Solve Exponential Equations using Logs.
EQ: How do you use the properties of exponents and logarithms to solve equations?
Section 3.4. Solving Exponential Equations Get your bases alike on each side of the equation If the variable is in the exponent set the exponents equal.
Warm up. 3.4 Solving Exponential & Logarithmic Equations Standards 13, 14.
6.10/6.11 Laws of Logarithms and change of base formula.
6.6 – Solving Exponential Equations Using Common Logarithms. Objective: TSW solve exponential equations and use the change of base formula.
Logarithmic Functions. Examples Properties Examples.
Essential Questions: 1. How do I solve exponential functions? 2. How do I solve logarmithic functions?
Solving Logarithmic Equations. Solving an Exponential Equation Ex. 7 3x =20 log 7 20=3x ≈3x x≈.5132 Write in log form Evaluate in the calculator.
TODAY IN ALGEBRA… Warm Up: Review solving Multi-step equations 15 minutes: Finish Mid-Ch.3 Test Learning Goal: 3.4 You will solve equations with.
Warm – up #4. Homework Log Fri 2/5 Lesson 6 – 4 Learning Objective: To solve log and exponential equation Hw: #605 Pg. 369 #1 – 49 odd.
If m & n are positive AND m = n, then Can solve exponential equation by taking logarithm of each side of equation Only works with base 10.
PH. In any solution the H 3 O + and OH - concentration is always very small. pH- method of representing the H 3 O + concentration in a solution. pH =
11.3 – Exponential and Logarithmic Equations. CHANGE OF BASE FORMULA Ex: Rewrite log 5 15 using the change of base formula.
8.5 – Exponential and Logarithmic Equations. CHANGE OF BASE FORMULA where M, b, and c are positive numbers and b, c do not equal one. Ex: Rewrite log.
Section 7-5 Properties of Logarithms Objectives I can evaluate Common Logs using a calculator I can use Change Base Rule I can expand log expressions.
Solving Exponential and Logarithmic Equations Section 8.6.
3.2 Solving Equations by Using Addition and Subtraction Addition Property of Equality –If the same number is added to each side of an equation, the resulting.
Solving Quadratic Equations by Graphing. Essential Question Where are the solutions to quadratic equations located on the graph of the parabola?
Applications of Common Logarithms Objective: Define and use common logs to solve exponential and logarithmic equations; use the change of base formula.
Solving Logarithmic Equations Chapter 8.6. log with same base on both sides Use this property for logarithms with the same base: log b x = log b y if.
Properties of Logarithms: Lesson 53. LESSON OBJECTIVE: 1)Simplify and evaluate expressions using the properties of Logarithms. 2)Solve logarithmic equations.
TODAY IN ALGEBRA 2.0… REVIEW: 7.5 Expand and Condense LOGs COMPLETE: HW #6 Learning Target: 7.6 You will solve exponential equations by changing.
Using Inverse Matrices Solving Systems. You can use the inverse of the coefficient matrix to find the solution. 3x + 2y = 7 4x - 5y = 11 Solve the system.
Warm-Up: Simplify each of the following. Homework Solutions.
LOGS EQUAL THE The inverse of an exponential function is a logarithmic function. Logarithmic Function x = log a y read: “x equals log base a of y”
7-5 Logarithmic & Exponential Equations. Terms and Concepts these will be on a quiz.
LOGARITHMIC AND EXPONENTIAL EQUATIONS LOGARITHMIC AND EXPONENTIAL EQUATIONS SECTION 4.6.
Exponential and Logarithmic Equations. 1. Solve each exponential equation by expressing each side as a power of the same base and then equating exponents.
Solving Quadratic Equations – Quadratic Formula The following shows how to solve quadratic equations using the Quadratic Formula. A quadratic equation.
Section 11-5 Common Logarithms. Logarithms with base 10 are called common logarithms. You can easily find the common logarithms of integral powers of.
Solving Equations with the Variable on Each Side 2.4.
Chapter 3 Exponential and Logarithmic Functions 1.
Solving Exponential Equations. We can solve exponential equations using logarithms. By converting to a logarithm, we can move the variable from the exponent.
Algebraic Manipulations Worksheet Solutions. Q1Q2 Make x the subject of the given formula.
7.6 – Solve Exponential and Log Equations. Property of Equality for Exponential Equations If b is a positive number other than 1, then ___________ if.
WECHS – 13 December Given that log 2.72 = , approximate the following without a calculator: log 0.272, log 272, and log How would.
1. 2 Switching From Exp and Log Forms Solving Log Equations Properties of Logarithms Solving Exp Equations Lnx
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