Brilliant as always. I can see the error, Thank you. If I try solving this by rewriting the right side rather than the left side as a common base i.e. 5 ^12 --> 25^ 11 then n would have to be greater than 11 ? Your mistake is there. Arithmetic of powers do not work that way. 5^12 = 5*(5^11) NOT 25^1...

Roderick mixes a martini that has a volume of n ounces that is 40% vermouth and 60% gin by volume. He wants to change this so that it is 25% vermouth by volume. How many ounces of gin must he add? Let us assume n = 100 Hence, there is 40 ounce of vermouth and 60 ounce of gin. We have to make the ra...

I'm unclear about the very fist step of factoring 2^(x-2)[2^2 - 1] = 3(2^13)....how is 2^(x-2)a common factor? Good question. To answer this, let's examine some analogous factoring cases: k^5 - k^3 = k^3(k^2 - 1) m^19 - m^15 = m^15(m^4 - 1) Or how about: w^x + x^(x+5) = w^x(1 + w^5) Notice that, ea...

I'm unclear about the very fist step of factoring
2^(x-2)[2^2 - 1] = 3(2^13)....how is 2^(x-2)a common factor?

This requires some factoring.
2^x - 2^(x-2) = 3(2^13)
2^(x-2)[2^2 - 1] = 3(2^13)
2^(x-2)[3] = 3(2^13)
So, 2^(x-2)= 2^13
x-2 = 13
[spoiler]x = 15[/spoiler]

Yes, it was an error in typing the statements. Statement (2) should have read as sq rt 10d is NOT an integer. Thanks for the solution as I understand the solution now.

Sequences - DS

In the infinite sequence S, each term Sn after S2 is equal to the sum of the two terms Sn-1 and Sn-2. If S1 is 4, what is the value uf S2?

(1) S3 = 7
(2) S4 = 10[/quote][/list]