II wrote:5000000 = 3^t
.

irst of all, what is the source? This is strange question...

3 in any power will end with 3, 9, 7 or 1. Moreover, 5000000 is not divisible by 3

I think this Q must be written is such manner:

5000000 >= 3^t
what is the maximum value of t?

3^5 * 3^5 = 243 * 243 = approx. 60 000*3, => 180 000*3 = 540 000, =>540 000*3= appr 1 500 000, =>1 500 00*3 = 4 500 000

I think maximum value of t is 14

This isnt a question from any GMAT source ... I was just interested in how someone would approach this type of question. Also note, I asked what is the "approximate" value of t

I suppose I could have just stated:
16 = 2^t
What is t? And someone could easily answer this question manually.

If I stated
2000000 = 2^t ... what is the approximate value of t ... then how would you work that out ?

Thanks.

2^10 = approx 1000, so 2^20 = approx 1 000 000
2^21 = approx 2 000 000
In fact it will be more that 2 000 000 because I reduced 2^10 to approx 1000, 2^10 = 1024

So power is between 20 and 21
I dont know the exact answer. But I think it will be closer to 21 than to to 20

thanks.