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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!!.

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