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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