If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?

Question

If  3^a – 3^{(a – 2)} = 8(3^{27}) , what is the value of 2a ?

A. 20
B. 25
C. 27
D. 29
E. 58

BrentGMATPrepNow · Accepted Answer

Given:  3^a – 3^{(a – 2)} = 8(3^{27})

Factor  3^{(a – 2)}  from the left side to get:  3^{(a – 2)}(3^2 – 1) = 8(3^{27})

Evaluate the part in the brackets:  3^{(a – 2)}(8) = 8(3^{27})

Divide both sides by 8 to get:  3^{(a – 2)} = 3^{27}

This means:  a - 2 = 27

Solve: a = 29
So, 2a = (2)(29) = 58

Answer: E

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pushpitkc · Answer

Given  3^a – 3^{(a – 2)} = 8(3^{27}) , we have been asked to find the value of 2a.

8(3^{27}) = (3^2 - 1)(3^27) = 3^{2+27} - 3{27}

Therefore we know that  3^a – 3^{(a – 2)} = 3^{29} - 3{27} = 3^{29} - 3{(29 - 2)}

Therefore, a = 29 and  2a = 58(Option E)

TaN1213 · Answer

3^a - 3^(a-2) = 8(3^27)
3^a -(3^a/3^2) = 8(3^27)
take lcm = 3^2 and then cross multiply the denominator
(3^a)(3^2) - (3^a) = (3^2)(8)(3^27)
take (3^a) common on LHS
(3^a)  = (3^29)(8)
cancel 8 on both sides
(3^a) = (3^29)
a= 29
2a = 58
option E

niks18 · Answer

LHS:  3^a-\frac{3^a}{3^2}   = 3^a(1-\frac{1}{3^2})  =  3^a*\frac{8}{9} 
or,  3^{a-2}*8   = 8*3^{27} 
Hence  a-2=27  or  a=29 . Therefore  2a = 58

Option  E

JeffTargetTestPrep · Answer

We can simplify the given equation:

3^a - (3^a)(3^-2) = 8(3^27)

Factor 3^a from the left side:

3^a(1 - 1/9) = 8(3^27)

3^a(8/9) = 8(3^27)

3^a = 8(3^27) x 9/8

3^a = 3^27 x 3^2

3^a = 2^29

a = 29

So, 2a = 58.

Alternate Solution:

Observe that 3^a = 3^(a - 2 + 2) = (3^(a - 2))(3^2). Then:

(3^(a - 2))(3^2) - (3^(a - 2)) = 8(3^27)

Let’s factor the common 3^(a - 2) from the left side:

3^(a - 2)(3^2 - 1) = 8(3^27)

3^(a - 2)(8) = 8(3^27)

3^(a - 2) = 3^27

a - 2 = 27

a = 29

2a = 58

Answer: E

gps5441 · Answer

RHS
8 can be written as (9-1) or (3²-1)
8(3²⁷)=(3²-1)X(3²⁷)
=3²⁹-3²⁷
check answer choices.
Start with easy one.
let 2a=10 or a=5
plugin into LHS and check
3⁵-3³-Not correct
let 2a=58
a=29
Plugin to LHS of the equation
3²⁹-3²⁷=LHS=correct=E

gps5441 · Answer

RHS
8(3²⁷)=(3²-1)X(3²⁷)
=3²⁹-3²⁷
check answer choices.
Start with easy one.
let 2a=10 or a=5
plugin into LHS and check
3⁵-3³-Not correct
let 2a=58
a=29
Plugin to LHS of the equation
3²⁹-3²⁷=LHS=correct=E

Abhishek009 · Answer

Or,  3^a – 3^{(a – 2)} = 8(3^{27})

Or,  3^a – \frac{3^a}{3^2} = (3^2 - 1)(3^{27})

Or,  3^a*3^2 – 3^a = 3^2(3^2 - 1)(3^{27})

Or,  3^a(3^2 – 1) = 3^2(3^2 - 1)(3^{27})

Or,  3^a = 3^2(3^{27})

Or,  3^a = 3^{29}

Or,  a = 29 
  
So, 2a = 58 , answer will be (E)

bumpbot · Answer

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If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?

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If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?

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