Solve the equations and inequalities: frac{2^{x}}{3}leqfrac{5^{x}}{4}

Solve the equations and inequalities: frac{2^{x}}{3}leqfrac{5^{x}}{4}

Question
Logarithms
asked 2020-10-27
Solve the equations and inequalities: \(\displaystyle{\frac{{{2}^{{{x}}}}}{{{3}}}}\leq{\frac{{{5}^{{{x}}}}}{{{4}}}}\)

Answers (1)

2020-10-28
Take the logarithm of both sides of the inequality to remove the variable from the exponent. Inequality Form: \(\displaystyle{x}≥\frac{{{\ln{{\left({3}\right)}}}−{\ln{{\left({4}\right)}}}}}{{{\ln{{\left({2}\right)}}}−{\ln{{\left({5}\right)}}}}}\) Interval Notation: \(\displaystyle{\left[\frac{{{\ln{{\left({3}\right)}}}−{\ln{{\left({4}\right)}}}}}{{{\ln{{\left({2}\right)}}}−{\ln{{\left({5}\right)}}}}},∞\right)}\)
0

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