Ok...There are two ways to solve this problem...One is the use of Logs to find an unknown exponent. For example:
8^x=15
= log 15 base 8 = x (re-write in log form)
=log 15 / log 8 (divide)
=1.3022968652 (this is the "x" exponent)
8^y=25
=log 25 base 8 = y
=log 25 / log 8
= 1.54795206326 (this is the "y" exponent)
Plug your now Known exponents into your equation:
8^2x+y = 8^2(1.3022968652)+(1.54795206326) = 5624.9999 = 5625
Second Way:
They made this easy because of the same base 8.
8^x=15 , 8^y=25, 8^2x+y=??
8^2x+y = 8^2x * 8^y (re-write by seperating exponents)
8^y is the easy part, we know that is 25
8^2x is not the same of course as 8^x (which we know is 15) so what makes it different? Yes the "2". Well you squared the left side of the equation so you have to square the right side: 8^2x = 15^2. Now you know 8^2x = 225 (15 squared).
So put the two together: 8^2x * 8^y is now the same as 225*25 = 5625
^ = raised to that exponent
* = multiplication
I hope this helps. It is a tough problem to explain on a message board.
Best regards,
Jason
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