Posted by Jake on Sunday, January 29, 2012 at 1:55am.
Solve for x: 6^(x+3) - 6^x = 215.
I got answer as 1, is it correct?
Precalculus - Bosnian, Sunday, January 29, 2012 at 3:33am
No it isn't.
The correct answer is x = 0
6 ^ ( x + 3 ) = 6 ^ ( 0 + 3 ) = 6 ^ 3 = 216
6 ^ x = 6 ^ 0 = 1
216 - 1 = 215
Precalculus - Jai, Sunday, January 29, 2012 at 4:50am
Bosnian's answer is correct. I'll just show how to get 0.
6^(x+3) - 6^x = 215
recall that when multiplying exponents of the same base, we add their exponents. for example,
x^2 * x^4 = x^(2+4) = x^6
now we do the opposite to 6^(x+3). we'll separate this into,
6(x+3) = 6^x * 6^3
now we rewrite the equation,
6^x * 6^3 - 6^x = 215
then, we factor the 6^x:
(6^x)(6^3 - 1) = 215
(6^x)(216-1) = 215
(6^x)(215) = 215
6^x = 1
this equation is only true if x = 0, since any number (except zero) raised to 0 is equal to 1.
hope this helps~ :)
Precalculus - Reiny, Sunday, January 29, 2012 at 8:59am
let y = 6^x
then our equation becomes
6^3(6^x) - 6^x = 215
216y - y = 215
215y = 215
y = 215/215 = 1
so 6^x = 1
x = 0
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