Question

Solve for x: 6^(x+3) - 6^x = 215.

I got answer as 1, is it correct?

Answer 1

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

Answer 2

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~ :)

Answer 3

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