Solve the equation. Do not use a calculator. log ⁡ 6 ( 2 x + 9 ) = log ⁡ 6 ( 4 x + 5 ) \log _ { 6 } ( 2 x + 9 ) = \log _ { 6 } ( 4 x + 5 ) lo g 6 ( 2 x + 9 ) = lo g 6 ( 4 x + 5 ) A) x = 2 x = 2 x = 2 B) x = − 7 x = - 7 x = − 7 C) x = 7 x = 7 x = 7 D) x = − 2 x = - 2 x = − 2 E) no solution

Question

Solve the equation. Do not use a calculator.   log ⁡ 6 ( 2 x + 9 )  = log ⁡ 6 ( 4 x + 5 )  \log _ { 6 } ( 2 x + 9 )  = \log _ { 6 } ( 4 x + 5 )  lo g 6 ​ ( 2 x + 9 )  = lo g 6 ​ ( 4 x + 5 )  A)    x = 2 x = 2 x = 2 B)    x = − 7 x = - 7 x = − 7 C)    x = 7 x = 7 x = 7 D)    x = − 2 x = - 2 x = − 2 E) no solution

Rakan Alfouzan · Accepted Answer

Final Answer : A, Explanation :   Since the bases of the logarithms are the same, the arguments must be equal. Thus,   2 x + 9 = 4 x + 5 2x + 9 = 4x + 5 2 x + 9 = 4 x + 5  . Solving for   x x x   gives   x = 2 x = 2 x = 2  .

Solve the equation. Do not use a calculator. $log _ { 6 } ( 2 x + 9 ) = \log _ { 6 } ( 4 x + 5 )$

A) $x = 2$
B) $x = - 7$
C) $x = 7$
D) $x = - 2$
E) no solution

Definitions

Learning Objectives

Learning Objectives

Related questions

Solve the equation. Do not use a calculator. log⁡6(2x+9) =log⁡6(4x+5) \log _ { 6 } ( 2 x + 9 ) = \log _ { 6 } ( 4 x + 5 ) log6​(2x+9) =log6​(4x+5) A) x=2x = 2x=2 B) x=−7x = - 7x=−7 C) x=7x = 7x=7 D) x=−2x = - 2x=−2 E) no solution

Definitions

Learning Objectives

Learning Objectives

Related questions

Solve the equation. Do not use a calculator. $log _ { 6 } ( 2 x + 9 ) = \log _ { 6 } ( 4 x + 5 )$

A) $x = 2$
B) $x = - 7$
C) $x = 7$
D) $x = - 2$
E) no solution