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# [Smart Math] Algebra Problem 3

Here’s and example of a SMART MATH problem for ALGEBRA.

### Problem

Find the value of ‘1’ in $2^{4a+4}=4^{2a+1}+12$.

1. 4
2. 2
3. 1
4. 3
5. 0

### The Usual Method

$2^{4a}\times 2^{4}=4^{2a}\times 4+12$

$\therefore$ $2^{4a}\times 2^{4}=2^{4a}\times 2^{2}+12$

$\therefore$ $2^{4a}\times 2^{4}-2^{4a}\times 2^{2}=12$

$\therefore$ $2^{4a}\times 2^{2}$ ($2^{2}-1$) = 12

$\therefore$ $2^{4a}\times 4\times 3=12$

$\therefore$ $2^{4a}$ = 1

$\therefore$ a = 0

(Ans: 5)

Estimated Time to arrive at the answer = 75 seconds.

### Using Technique

Simply look at the options and start substituting the values in the expressions and just check which one satisfies the equation Also, remember to start substituting with the value that is easiest of all to substitute. In this case, for example, the easier values are ‘0’ and ‘1’. You would notice that ‘0’ satisfies the equation as follows:

$2^{4(0)+4}=4^{2(0)+1}+12$

$2^{4}=4^{1}+12$

$2^{4}=4+12=16$

Hence option ‘5’.

(Ans: 5)

Estimated Time to arrive at the answer = 10 seconds.
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