For integers a and b, 16a=32b. Which of the following correctly expres

Question

For integers a and b, 16a = 32^b. Which of the following correctly expresses a in terms of b?

A. a = 2^b
B. a = 4^b
C. a = 2^(5b − 4)
D. a = 4^(5b − 4)
E. a = 2^(5b)

Kudos for a correct  solution .

Ankur9 · Answer

16a = 32^b 
 2^4 a = (2^5)^b 
a = (2)^(5b-4)

LaxAvenger · Answer

I tried this one with an example, although I am not quite sure if this is correct. I would appreciate if there would be a common rule for this.

I tried it out with b = 2 and only c correctly expresses the following:

16a = 32^b b = 2
16a = 1024
a = 64

choice c --> a = 2^6 = 64

However, this is a quite time consuming process. Is there something faster?

Answer C

kdatt1991 · Answer

I think it is C! Here's my solution: 16a = 32^b...... this is the same as (2^4)*a = (2^(5*b)). Therefore after simplifying this equation we get (2^4)*a = (2^5b)...... and thus a = (2^5b)/ (2^4). According to the rules of exponents (2^5b)/ (2^4) = 2^(5b − 4). Hence a = 2^(5b − 4). Please consider giving me KUDOS if you felt this post was helpful! Thanks.

TudorM · Answer

Hi Bunuel,

This is an exponent problem

we translate the equality into:

(2^4)*a = (2^5)^b =>
a = (2^5*b)/2^4 =>
a = 2^5b-4

CORRECT ANSWER C

chetan2u · Answer

Hi
ans C..
 
it is better if u get the values on the two sides to its basic form..
16a = 32^b... 
 a*2^4=2^5b..
a=2^(5b-4)...

eddyki · Answer

a=32^b/16
a=(2^(5b))/(2^4)
since x^m/x^n=x^(m-n)
we can go for a=2^(5b-4)

C!

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

This problem tests core exponent rules. First, remember the Guiding Principles of Exponents, which start with:

Find common bases.

You can express 16a=32^b as 2^4*a=(2^5)^b. Then, using core exponent rules, you can multiply 5 by b to get:

2^4*a=2^(5b)
Now you can isolate a by dividing both sides by 24. That leaves:

a=2^(5b)/2^4
At this point, you should remember that when you divide exponents of the same base, you subtract the exponents (numerator minus denominator). That leaves:

a=2^(5b−4), the correct answer.

bumpbot · Answer

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For integers a and b, 16a=32b. Which of the following correctly expres

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For integers a and b, 16a=32b. Which of the following correctly expres

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