University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

441

Pages:

5
Author:

Jazmine Summers

Solving Exponential and Logarithmic Equations For use with Exploration 6.6 Essential Question How can you solve exponential and logarithmic equations? 1 EXPLORATION: Solving Exponential and Logarithmic Equations Work with a partner. Match each equation with the graph of its related system of equations. Explain your reasoning. Then use the graph to solve the equation. a. 2^x = 2 Notetaking with Vocabulary For use after Lesson 6.6 In your own words, write the meaning of each vocabulary term. exponential equations logarithmic equations 1 Core Concepts Property of Equality for Exponential Equations Algebra If b is a positive real number other than 1, then (\mathfrak{b}^{x}=\mathfrak{b}^{y}) if and only (if|x=y.) Example If (3^{x}=3^{5}.) then (x=5. 1f|x=5) then (3^{x}=3^{5}.) Property of Equality for Logarithmic Equations Algebra (\begin{matrix}If~b,x_{s}\ x=y.\end{matrix}) and y are positive real numbers with b 1, then log,xlog, if and only if Example If (log_{2}x=log_{2}7,) then (x=7.) If then (log_{2}x=log_{2}7.) [x=f_{r}] Goouth 2 Decay Extra Practice In Exercises 1-6, solve the equation. 5^(2x+4) = 5^(5x-8) 4^(2x-1) = 8^(x+2) (2^2)^(2x-1) = (2^3)^(x+2) 2(2x-1) = 3(x+2) 4x-2 = 3x+6 x = 8 x + 3 = log_3 5 x = log_3 5 - 3 (1/5)^(3x-2) = √(25^x) (5^-1)^(3x-2) = (5^2)^(x/2) -1(3x-2) = 2 * x * (1/2) -3x+2 = x 2 = 4x 1/2 = x 12e^(1-x) = 500 e^(1-x) = 125/3 1-x = ln(125/3) -x = ln(125/3) - 1 x = 1 - ln(125/3) -14 + 3e^x = 11 3e^x = 25 e^x = 25/3 x = ln(25/3)