Waste less time on Facebook — follow Brilliant.
Already have an account? Log in here.
Logarithmic Inequalities
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:
\[ [ \ln ( \ln 2 ) ] ^2 \text { or } [ \ln ( \ln 3) ]^2 ? \]
Already have an account? Log in here.
by
Calvin Lin
Find the range of positive value of \(x\) such that \(\log_3 (x+7) < \log_9(x^2+77) \) is fulfilled?
Already have an account? Log in here.
by
Denton Young
Which of the following logarithms is greater?\[\color {green}{\log _{9}{71}} ~~~~\text{or}~~~~\color {blue}{\log _{8}{61}}\]
Already have an account? Log in here.
by
Rohit Udaiwal
\[ \ln\left(2x^{2} - 3x + 8\right) \le \dfrac{\ln\left(x^{4}+4x^{3} + 8x^{2} + 8x + 4\right)}{2} \]
Find the product of all integer values of \( x \) which satisfy the inequality above.
Already have an account? Log in here.
by
Vighnesh Shenoy
True or false:
For \(1<x<2\), the inequality \( \log_{10} (x+99) > x\) is satisfied.
Already have an account? Log in here.
by
Denton Young