If 3^6x = 8,100, what is the value of [3^(x - 1)]^3 ?
A. 90
B. 30
C. 10
D. 10/3
E. 10/9
Firstly, i'm not sure how to break down 8100 into 3^6x. 3^4 =81 but what is the value of the power of 3 to get 8100??
Can someone show simplified steps to this problem. thanks
If 3^6x = 8,100, what is the value of [(3^x – 1)]^3 ?
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my shy attempt
3^(6x)=8100
3^(6x)=3^4*100
3^(6x-4)-10^2=0
3^(3x-2)*2-10^2=0
(3^(3x-2)-10)*(3^(3x-2)+10)=0 only 1st braket has sence
3^(3x-2)=10
[3^(x - 1)]^3 ? - think it must be 3^(x-1)*3=3^(3x-3)
3^(3x-2)=3^(3x-2+3-3)=3^(3x-3)+1=3^(3x-3)*3
3^(3x-3)*3=10
3^(3x-3)=10/3
so i got D
what is oa?
3^(6x)=8100
3^(6x)=3^4*100
3^(6x-4)-10^2=0
3^(3x-2)*2-10^2=0
(3^(3x-2)-10)*(3^(3x-2)+10)=0 only 1st braket has sence
3^(3x-2)=10
[3^(x - 1)]^3 ? - think it must be 3^(x-1)*3=3^(3x-3)
3^(3x-2)=3^(3x-2+3-3)=3^(3x-3)+1=3^(3x-3)*3
3^(3x-3)*3=10
3^(3x-3)=10/3
so i got D
what is oa?
- stephen@knewton
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Crasher,
The key to your question from GMATprep is to recognize that because your variable appears within an exponent on base 2, you need to "create" a 3 somewhere on the left side of the equation. That way, you'll be able to cancel the 3s and compare the exponents of like bases.
You must also recognize the rule of exponents that (2^X)(2^Y) = 2^(X+Y) ... to help you remember that, recall that two squared times two squared is simply "two times two times two times two" or two to the fourth.
[apologies for spelling out the powers, y'all, I think it's often easier than using carrots to denote superscript].
Now ... with this problem, is there something you can factor out of the left side that will result in a 3 multiplied by a power of 2?? Answer follows as a spoiler, for anybody that wants to try it!
[spoiler]
If you factor 2^(X-2) out of the left side, you end up with [2^(X-2)](2^2 + 1) or 3[2^(X-2)]. The threes cancel, and that allows you to set the exponents equal. X-2 = 13 ... and you can take it from there![/spoiler]
Hope that helps! Steve
The key to your question from GMATprep is to recognize that because your variable appears within an exponent on base 2, you need to "create" a 3 somewhere on the left side of the equation. That way, you'll be able to cancel the 3s and compare the exponents of like bases.
You must also recognize the rule of exponents that (2^X)(2^Y) = 2^(X+Y) ... to help you remember that, recall that two squared times two squared is simply "two times two times two times two" or two to the fourth.
[apologies for spelling out the powers, y'all, I think it's often easier than using carrots to denote superscript].
Now ... with this problem, is there something you can factor out of the left side that will result in a 3 multiplied by a power of 2?? Answer follows as a spoiler, for anybody that wants to try it!
[spoiler]
If you factor 2^(X-2) out of the left side, you end up with [2^(X-2)](2^2 + 1) or 3[2^(X-2)]. The threes cancel, and that allows you to set the exponents equal. X-2 = 13 ... and you can take it from there![/spoiler]
Hope that helps! Steve
Stephen
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Oops I creat confusion here.
Actually I was concerned about this thread's main post question.
3^6x = 8,100, what is the value of [(3^x - 1)]^3
How do we solve this problem from X, where we have 2 different base?
Actually I was concerned about this thread's main post question.
3^6x = 8,100, what is the value of [(3^x - 1)]^3
How do we solve this problem from X, where we have 2 different base?
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We are given that 3^6x = 8100 and asked to find (3^(x-1))^3 = 3^(3x - 3)mitzwillrockgmat wrote:If 3^6x = 8,100, what is the value of [3^(x - 1)]^3 ?
A. 90
B. 30
C. 10
D. 10/3
E. 10/9
Firstly, i'm not sure how to break down 8100 into 3^6x. 3^4 =81 but what is the value of the power of 3 to get 8100??
Can someone show simplified steps to this problem. thanks
Since 3^6x = 8100 , 3^3x = 90
3^(3x-3)= 90/3^3 =10/3
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this question is part of a set of mock gmat exams prepared a gmat prep centre called, 'jamboree'. im not a student there & a friend passed it along. im putting up a image of the question to make it easier to read.Patrick_GMATFix wrote:question source plz
pls give your feedback on how to solve! thanks
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kevincanspain wrote:Hello there! can you please elaborate here , how did u break downmitzwillrockgmat wrote:If 3^6x = 8,100, what is the value of [3^(x - 1)]^3 ?
A. 90
B. 30
C. 10
D. 10/3
E. 10/9
Firstly, i'm not sure how to break down 8100 into 3^6x. 3^4 =81 but what is the value of the power of 3 to get 8100??
Can someone show simplified steps to this problem. thanks
3^6x = 8100 into 3^3x = 90
3^(3x-3)= 90/3^3 =10/3
thanks
- jeffedwards
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mitzwillrockgmat wrote: Hello there! can you please elaborate here , how did u break down
3^6x = 8100 into 3^3x = 90
3^(3x-3)= 90/3^3 =10/3
thanks
mitzwillrockgmat, hope this breakdown is understandable
3^6x = 8100
(3^3x)^2 = 8100 (pulled the 2 out of the left side to make visible)
(3^3x)^2 =90^2 (made the right side similar)
3^3x = 90 (we get this by taking the square root of both sides...to get rid of the squares)
Now we want to add the -3 in the exponent to make this equation the same as the question
(3^3x)(3^-3) = 90(3^-3) (multiply both sides by 3^-3)
3^(3x-3) = 90(3^-3) (combined on the left side; now we just need to simplify the right to get our answer)
90(3^-3)
90/27 (because 3^-3 is equal to 1/(3^3) or 1/27)
10/3 (simplified fraction by dividing both numbers by 9)
Hope that helps.
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to solve these type of problem always try to convert expression in given format then u can solve it very fast
here 3^6x=8100,so (3^3x)^2=8100
hence 3^3x=90
now we have to find (3^3x-1)^3=3^3x-3=3^3x/3^3=3^3x/27=90/27=10/3 ans
quantskillsgmat
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always be one step ahead
here 3^6x=8100,so (3^3x)^2=8100
hence 3^3x=90
now we have to find (3^3x-1)^3=3^3x-3=3^3x/3^3=3^3x/27=90/27=10/3 ans
quantskillsgmat
wisdommart delhi
always be one step ahead