Answer :
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!!.
