examples, and problems from the community.

including olympiad champions, researchers, and professionals.

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

Logarithmic inequalities are useful in analyzing situations involving repeated multiplication, such as interest and exponential decay.

It is well known that \( \ln 2 < \ln 3 \). Which of the following is bigger:

\[ [ \ln ( \ln 2 ) ] ^2 \text { or } [ \ln ( \ln 3) ]^2 ? \]

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Calvin Lin**

Are you sure you want to view the solution?

Cancel
Yes I'm sure

Find the range of positive value of \(x\) such that \(\log_3 (x+7) < \log_9(x^2+77) \) is fulfilled?

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Denton Young**

Are you sure you want to view the solution?

Cancel
Yes I'm sure

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Rohit Udaiwal**

Are you sure you want to view the solution?

Cancel
Yes I'm sure

\[ \ln\left(2x^{2} - 3x + 8\right) \le \dfrac{\ln\left(x^{4}+4x^{3} + 8x^{2} + 8x + 4\right)}{2} \]

Find the product of all integer values of \( x \) which satisfy the inequality above.

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Vighnesh Shenoy**

Are you sure you want to view the solution?

Cancel
Yes I'm sure

**True or false**:

For \(1<x<2\), the inequality \( \log_{10} (x+99) > x\) is satisfied.

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Denton Young**

Are you sure you want to view the solution?

Cancel
Yes I'm sure

×

Problem Loading...

Note Loading...

Set Loading...