3^X-3^(X-1)=162 ?!?1

[fahadmuhammad86]

Im having a hard time figuring this question out:

3^X-3^(X-1)=162 What is x(x-1)=?

Answer is 16.

Can anyone explain how to do this question?

[nitin_prakash_khanna]

given
3^x-3^(x-1) = 162
lets first simplify the left side.

3^x- {3^x*3^-1}= 3^x-(3^x)/3
3^x {1-(1/3)}
3^x*2/3 = 162= 2*81= 2*3^4

This implies
x-1 = 4
so x=5

x*x-1 = 5*4 =20

Not sure why the answer is 16, can you please re check and post it here.

[rambabu]

For the a given question, answer must be 20.
I guess, either the stated answer or given question would be wrong.

[RonPurewal]

For the a given question, answer must be 20.
I guess, either the stated answer or given question would be wrong.

yeah, 16 is the wrong answer; it should be 20.

by the way, if you are not absolutely amazing at algebra, it's much easier to figure out the value of x by simply throwing in values until 3^x - 3^(x-1) comes out as 162. (shouldn't take too long -- just adjust upward if you get less than 162, and downward if you get more.)