If 27^(1/m) = 3^(3m) and 4m 1, then what is the value of m ?

Question

If  \sqrt {27} = 3^{3m}  and 4m > 1, then what is the value of m ?

(A) –1
(B) –1/4
(C) 0
(D) 1/4
(E) 1

Archit3110 · Answer

for 4m > 1
m=1
IMO E

vargamartin1031 · Answer

How do you get to m=1 from 4m > 1 ?

Archit3110 · Answer

vargamartin1031 
given 4m>1
browsing answer options we can say m has to be 1 then only 4*1>1 is valid

edlc313 · Answer

This can be rewritten as  3^{3/m} = 3^{3m}

We see here that 1 is really the only number that works here.

Using 4m > 1, we can easily see that 1 must be the answer

devavrat · Answer

what happened to m root of 27 ??
How does 1 satisfy this equation?
1 satisfies only 4m>1
If m is put in the m root 27 = 3^3m equation how can the equation be solved???
Pls explain

edlc313 · Answer

It looks like you'll need to brush up on exponents.

\sqrt {27}  =  (3^{3})^{1/m} = 3^{3*(1/m)} = 3^{3/m}

They're telling us that  3^{3/m} = 3^{3m}

For which answer choices does m satisfy 4m > 1?
 (A) –4 > 1
(B) –1 > 1
(C) 0 > 1
(D) 1 > 1 
 (E) 1

3^{3/m} = 3^{3m}  if we use 1 or -1 for m (using 0 gives us an invalid equation). So if we know that 4m > 1, then E must be the answer.

ScottTargetTestPrep · Answer

Rewriting the equation, we have:

3^(3/m) = 3^(3m)

3/m = 3m

3 = 3m^2

1 = m^2

m = 1 or m = -1

However, since 4m > 1, m must be 1.

Alternate solution:

Since 4m > 1, m > 1/4. Looking at the multiple choices, only choice E can be correct.

Answer: E

jamalabdullah100 · Answer

I got to:

27^(1/m) = 3^(3m)
(3^3)^1/m = (3^3)^m

So surely based on the above 1/m = m which means m can only be 1 so E is the answer. However, is this thought process correct?

bumpbot · Answer

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If 27^(1/m) = 3^(3m) and 4m > 1, then what is the value of m ?

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