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Math Help - Exponential Functions

  1. #1
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    Question Exponential Functions

    "Solve the equation: 16^n < 8^n+1"

    So far, I got this:

    (2^4)^n < (2^3)^n+1 --------- rewrote with a base of two
    4n < 3(n+1) ------------------ property of equality for exponential functions
    4n < 3n+3 ---------- as far as I could get

    The solution in the text is n < 3, but I don't understand how this could be? I've tried dividing the left and right side by 4, but that would cause me to end up in error with n > 3/4n+3/4.

    Thanks in advance.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mulya66 View Post
    "Solve the equation: 16^n < 8^n+1"

    So far, I got this:

    (2^4)^n < (2^3)^n+1 --------- rewrote with a base of two
    4n < 3(n+1) ------------------ property of equality for exponential functions
    4n < 3n+3 ---------- as far as I could get

    The solution in the text is n < 3, but I don't understand how this could be? I've tried dividing the left and right side by 4, but that would cause me to end up in error with n > 3/4n+3/4.

    Thanks in advance.
    just subtract 3n from both sides of the inequality
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  3. #3
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    ...I thought there was a rule of some sort? That way, I may apply the rule to similar problems. I suppose I'm making it more complicated than it seems...
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mulya66 View Post
    ...I thought there was a rule of some sort? That way, I may apply the rule to similar problems. I suppose I'm making it more complicated than it seems...
    you treat inequalities just like equal signs except in two cases.

    you turn them the other way if:
    1) you multiply through by a negative number
    2) you take the inverse of both sides of the inequality
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