IDNLearn.com makes it easy to find the right answers to your questions. Ask any question and get a detailed, reliable answer from our community of experts.
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 appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for trusting IDNLearn.com with your questions. Visit us again for clear, concise, and accurate answers.
