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It is well known that ln2<ln3 \ln 2 < \ln 3 ln2<ln3. Which of the following is bigger:
[ln(ln2)]2 or [ln(ln3)]2? [ \ln ( \ln 2 ) ] ^2 \text { or } [ \ln ( \ln 3) ]^2 ? [ln(ln2)]2 or [ln(ln3)]2?
Inspiration, see solution.
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Find the range of positive value of xxx such that log3(x+7)<log9(x2+77)\log_3 (x+7) < \log_9(x^2+77) log3(x+7)<log9(x2+77) is fulfilled?
Which of the following logarithms is greater?log971 or log861\color{#20A900}{\log _{9}{71}} ~~~~\text{or}~~~~\color{#3D99F6}{\log _{8}{61}}log971 or log861
ln(2x2−3x+8)≤ln(x4+4x3+8x2+8x+4)2 \ln\left(2x^{2} - 3x + 8\right) \le \dfrac{\ln\left(x^{4}+4x^{3} + 8x^{2} + 8x + 4\right)}{2} ln(2x2−3x+8)≤2ln(x4+4x3+8x2+8x+4)
Find the product of all integer values of x x x which satisfy the inequality above.
True or false:
For 1<x<21<x<21<x<2, the inequality log10(x+99)>x \log_{10} (x+99) > xlog10(x+99)>x is satisfied.
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