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  1. #1
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    what to do then?

    I tried to solve this exponential inequation , but i can't do more:

    5 625

    5*2^6/x>=625 dived by 5
    2^6/x>=125
    2^6/x>=5^3 and i have not idea what to do then
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  2. #2
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    Quote Originally Posted by MathE1 View Post
    I tried to solve this exponential inequation , but i can't do more:

    5 625

    5*2^6/x>=625 dived by 5
    2^6/x>=125
    2^6/x>=5^3 and i have not idea what to do then
    1. Multiply by x (according to the first line x > 0):

    2^6 \geq 5^3 \cdot x~\implies~x\leq\frac{2^6}{5^3} and  \frac{2^6}{5^3}= \frac{4^3}{5^3} = \left(\frac45\right)^3 = 0.512
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  3. #3
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    Quote Originally Posted by earboth View Post
    1. Multiply by x (according to the first line x > 0):

    2^6 \geq 5^3 \cdot x~\implies~x\leq\frac{2^6}{5^3} and  \frac{2^6}{5^3}= \frac{4^3}{5^3} = \left(\frac45\right)^3 = 0.512
    thanks earboth but i did one mistake
    it's 2^(6/X)>=5^3
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  4. #4
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    please help, in this inequation!
    2^(6/X)>=5^3
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  5. #5
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    Quote Originally Posted by MathE1 View Post
    please help, in this inequation!
    2^(6/X)>=5^3
    2^{\frac6x} \geq 5^3

    Take the inequality to the power of \frac x6:

    \left(2^{\frac6x}\right)^{\frac x6} \geq \left(5^3\right)^{\frac x6}~\implies~2 \geq 5^{\frac x2} Now square the both sides of the inequality:

    4 \geq 5^x~\implies~\log_5(4) \geq x

    To get an approximate result use the base-change-formula:

    x\leq \log_5(4) and \log_5(4)=\dfrac{\ln(4)}{\ln(5)}\approx 0.861...
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