LESSON 7 4 Solving Logarithmic Equations and Inequalities

LESSON 7– 4 Solving Logarithmic Equations and Inequalities

Over Lesson 7– 3 1 Write 4– 3 = __ in logarithmic form. 64 A. log– 3 4 = 1 __ 64 1 B. log– 3 __ =4 64 C. log 4 1 __ 64 = – 3 1 D. log 4 – 3 = __ 64

Over Lesson 7– 3 Write log 6 216 = 3 in exponential form. A. 63 = 216 B. 36 = 216 C. D.

Over Lesson 7– 3 Graph f(x) = 2 log 2 x. A. ans C. B. ans D.

Over Lesson 7– 3 Graph f(x) = log 3 (x – 4). A. C. B. D.

Over Lesson 7– 3 A. B. C. D.

Targeted TEKS A 2. 5(B) Formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation. A 2. 5(D) Solve exponential equations of the form y = abx where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions. Also addresses A 2. 5(E). Mathematical Processes A 2. 1(F), Also addresses A 2. 1(E).

You evaluated logarithmic expressions. • Solve logarithmic equations. • Solve logarithmic inequalities.

• logarithmic equation • logarithmic inequality

Solve a Logarithmic Equation Solve Original equation Definition of logarithm 8 = 23 Power of a Power Answer: x = 16

Solve A. n = B. n = 3 C. n = 9 D. n = .

Solve a Logarithmic Equation Solve log 4 x 2 = log 4 (– 6 x – 8). A. 4 B. 2 C. – 4, – 2 D. no solutions Read the Item You need to find x for the logarithmic equation. Solve the Item log 4 x 2 = log 4 (– 6 x – 8) x 2 = (– 6 x – 8) Original equation Property of Equality for Logarithmic Functions

Solve a Logarithmic Equation x 2 + 6 x + 8 = 0 (x + 4)(x + 2) = 0 x + 4 = 0 or x + 2 = 0 x = – 4 x = – 2 Subtract (– 6 x – 8) from each side. Factor. Zero Product Property Solve each equation.

Solve a Logarithmic Equation Check Substitute each value into the original equation. x = – 4 2 ? log 4 (– 4) = log 4 [– 6(– 4) – 8)] log 4 16 = log 4 16 x = – 2 2 ? log 4 (– 2) = log 4 [– 6(– 2) – 8)] log 4 4 = log 4 4 Answer: The solutions are x = – 4 and x = – 2. The answer is C.

Solve log 4 x 2 = log 4 (x + 20). A. 5 and – 4 B. – 2 and 10 C. 2 and – 10 D. no solutions