2^x - 2^(x-2) = 3(2^13)
Using the exponent rule x^a * x^b = x^(a+b):
2^x - 2^x*2^-2 = 3(2^13)
Factor out 2^x from the left side:
2^x (1 -2^-2) = 3(2^13)
Simplify:
2^x * (1 - 1/4) = 3(2^13)
2^x * 3/4 = 3(2^13)
Multiply both sides by 4 or 2^2:
2^x * 3 = 2^2 * 3(2^13)
Divide both sides by 3:
2^x = 2^2 * 2^13
Simplify:
2^x = 2^(2+13)
2^x = 2^15
Since the bases are the same you can say that x = 15
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exponents
Source: Beat The GMAT — Problem Solving |
what value did you bring to the discussion with that statement?vivek.kapoor83 wrote:clearly 15.
If it so clear that the answer is 15, please show your work.
2^x - 2^(x-2) = 3(2^13)
let us first solve the LHS
= 2^x - 2^x/ 2^2 solving by equating the denominator we get
= (2^x* 2^2 - 2^x) / 2^2
= [2^x * ( 2^2-1)] / 2^2
= [2^x * ( 4-1 ) ] / 2^2
= [ 2^x * ( 3 ) ] / 2^2
Now equating LHS and RHS we get
2^x * ( 3 ) = 3* (2^13 * 2^2)
2^x * ( 3) = 3* 2^15
cancelling 3 from both the sides and then comparing the exponents of 2 we get
x=15
I know this is too elaborate explanation but i am sure this shud clear most doubts.
let us first solve the LHS
= 2^x - 2^x/ 2^2 solving by equating the denominator we get
= (2^x* 2^2 - 2^x) / 2^2
= [2^x * ( 2^2-1)] / 2^2
= [2^x * ( 4-1 ) ] / 2^2
= [ 2^x * ( 3 ) ] / 2^2
Now equating LHS and RHS we get
2^x * ( 3 ) = 3* (2^13 * 2^2)
2^x * ( 3) = 3* 2^15
cancelling 3 from both the sides and then comparing the exponents of 2 we get
x=15
I know this is too elaborate explanation but i am sure this shud clear most doubts.
