The easiest approach would be to plug in the answers, which the GMAT would provide.oxfordbound wrote:Hi All,
I understand most algebra problems that have exponents (equivocate the bases and solve). But I ran into a problem from the Veritas Algebra book and the feedback provided from the Veritas book/forums wasn't up to par.
I'd like some real step by step guidance on this problem:
3^x - 3^x-1 = 2(3^13)
the answer is 14. I've worked through the problem as it has been laid out in the book but I cannot understand the methodology entirely in order to apply it to another problem.
The book denotes that you can factor out a 3^x OR (more efficiently) factor out a 3^x-1.
3^x-1 (3-1) = 2(3^13)
3^x-1(2) = 2(3^13)
x-1 = 13
x = 14
I don't fully understand this logic, can someone please clarify the underlying math logic/rules applied that is going on here please?
Thanks in advance,
Oxford Bound
Answer choice: x=15
3¹� - 3¹�ˉ¹ = 2 * 3¹³
3¹� - 3¹� = 2 * 3¹³
3¹�(3-1) = 2 * 3¹³
3¹� * 2 = 2 * 3¹³
The exponent on the left side is 1 more than the exponent on the right side.
Thus, we need to subtract 1 from x=15.
x = 15-1= 14.