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

Question
Logarithms
Solve the equations and inequalities: $$\frac{2^{x}}{3}\leq\frac{5^{x}}{4}$$

2020-12-26
Take the logarithm of both sides of the inequality to remove the variable from the exponent. Inequality Form: $$x≥(ln(3)−ln(4))/(ln(2)−ln(5))$$ Interval Notation: $$[(ln(3)−ln(4))/(ln(2)−ln(5)), ∞ )$$

### Relevant Questions

Solve the equations and inequalities: $$\displaystyle{\frac{{{2}^{{{x}}}}}{{{3}}}}\leq{\frac{{{5}^{{{x}}}}}{{{4}}}}$$
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Solve the equations and inequalities: $$\frac{2^{x}}{3} =\frac{5^{x}}{4}$$
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Solve the equations and inequalities below. Check your solution(s), if possible. $$\displaystyle{a}{.300}{x}-{1500}={2400}$$
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Solve the equations and inequalities below. Write your solutions in exact form. $$a. \frac{3}{4}-\frac{x}{3}=\frac{7x}{4}$$
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Solve the following equations and inequalities for x. Check your solution(s), if possible $$\displaystyle{a}.{\frac{{{3}}}{{{x}}}}={9}$$
$$\displaystyle{b}.\sqrt{{x}}={4}$$
$$\displaystyle{c}.{x}^{{{2}}}={25}$$
$$\displaystyle{d}.{2}{\left({x}−{3}\right)}{>}{4}$$