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Precalculus

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

I got answer as 1, is it correct?

  • Precalculus -

    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 -

    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 -

    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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