Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Select the equation that has the same solution as the equation below. 5⁽²ˣ⁻⁵⁾ = 125.
A. 3⁽⁵ˣ⁻¹⁾ = 81.
B. 64 = 2⁽³ˣ⁻⁶⁾.
C. 4⁽⁷ˣ⁺¹¹⁾ = 256.
D. 343 = 7⁽²ˣ⁺⁹⁾.

Sagot :

Answer:

[tex]\bold{B.\: 64=2^{3x-6}}[/tex]

Step-by-step explanation:

Solving the Problem

We must find the solution [tex]5^{2x-5}=125[/tex] to determine which of the answer choices is correct.

Knowing that 125 is the cubed value of 5 we can simplify and solve the equation.

                                          [tex]5^{2x-5}=5^3[/tex]

                                         [tex]2x-5=3[/tex]

                                     [tex]2x=8 \rightarrow x =4[/tex]

So, we must find an answer choice where its solution is x = 4!

[tex]\dotfill[/tex]

Finding the Right Answer Choice

Starting off with choice A, knowing that 81 is the same as [tex]9^2=(3^2)^2=3^4[/tex],

                                       [tex]3^{5x-1}=3^4[/tex]

                                       [tex]5x-1=4[/tex]

                                           [tex]5x=5\\x=1[/tex].

So, we eliminate A.

Going to B, knowing that 64 is the same as [tex]8^2=(2^3)^2=2^6[/tex],

                                       [tex]2^6=2^{3x-6}[/tex]

                                       [tex]6=3x-6[/tex]

                                         [tex]12=3x[/tex]

                                          [tex]4=x[/tex]

So, B is our final answer!

We can stop here since there can only be one correct answer, but let's solve the last two to verify that B is our answer.

Looking at C, knowing that 256 is the same as [tex]16^2=(4^2)^2=4^4[/tex],

                                  [tex]4^{7x+11}=4^4[/tex]

                                 [tex]7x+11=4[/tex]

                                     [tex]7x=-7[/tex]

                                      [tex]x=-1[/tex].

So, we eliminate C.

Solving D, knowing that 343 is the cubed value of 7,

                                     [tex]7^3=7^{2x+9}[/tex]

                                     [tex]3=2x+9[/tex]

                                      [tex]-6=2x[/tex]

                                       [tex]-3=x[/tex]

So, D is the wrong answer, and B must be our final answer!!.

We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.