Sign up to access problem solutions.

Already have an account? Log in here.

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:

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

Sign up to access problem solutions.

Already have an account? Log in here.

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

Sign up to access problem solutions.

Already have an account? Log in here.

Sign up to access problem solutions.

Already have an account? Log in here.

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

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

Sign up to access problem solutions.

Already have an account? Log in here.

**True or false**:

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

Sign up to access problem solutions.

Already have an account? Log in here.

×

Problem Loading...

Note Loading...

Set Loading...