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

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

2020-10-26
$$(2^x)/3=(5^x)/2^2$$
$$4(2^x)=3(5^x)$$
$$2^x+2=3*5^x$$

### Relevant Questions

Solve the equations and inequalities below, if possible. $$\displaystyle{a}.\sqrt{{{x}−{1}}}+{13}={13}$$
$$\displaystyle{b}.{6}{\left|{x}\right|}{>}{18}$$
$$\displaystyle{c}.{\left|{3}{x}-{2}\right|}\le{2}$$
$$\displaystyle{d}.{\frac{{{4}}}{{{5}}}}-{\frac{{{2}{x}}}{{{3}}}}={\frac{{{3}}}{{{10}}}}$$
$$\displaystyle{e}.{\left({4}{x}-{2}\right)}^{{{2}}}\le{100}$$
$$\displaystyle{f}.{\left({x}-{1}\right)}^{{{3}}}={8}$$
Solve the equations and inequalities: $$\displaystyle{\frac{{{2}^{{{x}}}}}{{{3}}}}={\frac{{{5}^{{{x}}}}}{{{4}}}}$$
Solve the equations and inequalities below. Check your solution(s), if possible. $$a.300x-1500=2400$$
$$b.(3/2)^{x}=(5/6)^{x}+2$$
$$c.x^{2}-25\leq 0$$
$$d.|3x-2|>4$$
Solve the equations and inequalities below. Check your solution(s), if possible. $$\displaystyle{a}{.300}{x}-{1500}={2400}$$
$$\displaystyle{b}.{\left(\frac{{3}}{{2}}\right)}^{{{x}}}={\left(\frac{{5}}{{6}}\right)}^{{{x}}}+{2}$$
$$\displaystyle{c}.{x}^{{{2}}}-{25}\leq{0}$$
$$\displaystyle{d}.{\left|{3}{x}-{2}\right|}{>}{4}$$
Solve the following equations and inequalities for x. Check your solution(s), if possible $$a. \frac{3}{x}=9$$
$$b. \sqrt x=4$$
$$c. x^{2}=25$$
$$d. 2(x−3)>4$$
Solve the equations and inequalities below. Write your solutions in exact form. $$a. \frac{3}{4}-\frac{x}{3}=\frac{7x}{4}$$
$$b. (b−4)2<12$$
$$c. ∣3+x∣−9\leq21$$
$$d. 5n^{2}−11n+2=0$$
Solve the following equations and inequalities for x. Check your solution(s), if possible $$\displaystyle{a}.{\frac{{{3}}}{{{x}}}}={9}$$
$$\displaystyle{b}.\sqrt{{x}}={4}$$
$$\displaystyle{c}.{x}^{{{2}}}={25}$$
$$\displaystyle{d}.{2}{\left({x}−{3}\right)}{>}{4}$$
Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. $$\frac{(x−4)}{(x+2)}\leq 0$$
Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. $$\displaystyle{\frac{{{\left({x}−{4}\right)}}}{{{\left({x}+{2}\right)}}}}\leq{0}$$
Solve the equations and inequalities. Write the answers to the inequalities in interval notation if possible. (A) $$|7x+4| + 11 = 2$$
(B) $$|7x + 4| + 11 < 2$$
(C) $$|7x + 4| + 11 > 2$$