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:
\([(ln(3)−ln(4))/(ln(2)−ln(5)), ∞ )\)

Question

asked 2020-10-27

Solve the equations and inequalities:
\(\displaystyle{\frac{{{2}^{{{x}}}}}{{{3}}}}\leq{\frac{{{5}^{{{x}}}}}{{{4}}}}\)

asked 2021-02-18

Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation.
\(\displaystyle{\log{{2}}}{\left({3}{x}−{1}\right)}={\log{{2}}}{\left({x}+{1}\right)}+{3}\)

asked 2020-10-25

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

asked 2020-11-22

Solve the equations and inequalities below, if possible.
\(\displaystyle{a}.\sqrt{{{x}−{1}}}+{13}={13}\)

\(\displaystyle{b}.{6}{\left|{x}\right|}{>}{18}\)

\(\displaystyle{c}.{\left|{3}{x}-{2}\right|}\le{2}\)

\(\displaystyle{d}.{\frac{{{4}}}{{{5}}}}-{\frac{{{2}{x}}}{{{3}}}}={\frac{{{3}}}{{{10}}}}\)

\(\displaystyle{e}.{\left({4}{x}-{2}\right)}^{{{2}}}\le{100}\)

\(\displaystyle{f}.{\left({x}-{1}\right)}^{{{3}}}={8}\)

\(\displaystyle{b}.{6}{\left|{x}\right|}{>}{18}\)

\(\displaystyle{c}.{\left|{3}{x}-{2}\right|}\le{2}\)

\(\displaystyle{d}.{\frac{{{4}}}{{{5}}}}-{\frac{{{2}{x}}}{{{3}}}}={\frac{{{3}}}{{{10}}}}\)

\(\displaystyle{e}.{\left({4}{x}-{2}\right)}^{{{2}}}\le{100}\)

\(\displaystyle{f}.{\left({x}-{1}\right)}^{{{3}}}={8}\)

asked 2021-02-12

Solve the equations and inequalities:
\(\displaystyle{\frac{{{2}^{{{x}}}}}{{{3}}}}={\frac{{{5}^{{{x}}}}}{{{4}}}}\)

asked 2021-02-08

Solve the equations and inequalities below. Check your solution(s), if possible.
\(a.300x-1500=2400\)

\(b.(3/2)^{x}=(5/6)^{x}+2\)

\(c.x^{2}-25\leq 0\)

\(d.|3x-2|>4\)

\(b.(3/2)^{x}=(5/6)^{x}+2\)

\(c.x^{2}-25\leq 0\)

\(d.|3x-2|>4\)

asked 2021-02-05

Solve the equations and inequalities below. Check your solution(s), if possible.
\(\displaystyle{a}{.300}{x}-{1500}={2400}\)

\(\displaystyle{b}.{\left(\frac{{3}}{{2}}\right)}^{{{x}}}={\left(\frac{{5}}{{6}}\right)}^{{{x}}}+{2}\)

\(\displaystyle{c}.{x}^{{{2}}}-{25}\leq{0}\)

\(\displaystyle{d}.{\left|{3}{x}-{2}\right|}{>}{4}\)

\(\displaystyle{b}.{\left(\frac{{3}}{{2}}\right)}^{{{x}}}={\left(\frac{{5}}{{6}}\right)}^{{{x}}}+{2}\)

\(\displaystyle{c}.{x}^{{{2}}}-{25}\leq{0}\)

\(\displaystyle{d}.{\left|{3}{x}-{2}\right|}{>}{4}\)

asked 2021-03-02

Solve the following equations and inequalities for x. Check your solution(s), if possible
\(a. \frac{3}{x}=9\)

\(b. \sqrt x=4\)

\(c. x^{2}=25\)

\(d. 2(x−3)>4\)

\(b. \sqrt x=4\)

\(c. x^{2}=25\)

\(d. 2(x−3)>4\)

asked 2021-03-11

Solve the equations and inequalities below. Write your solutions in exact form.
\(a. \frac{3}{4}-\frac{x}{3}=\frac{7x}{4}\)

\(b. (b−4)2<12\)

\(c. ∣3+x∣−9\leq21\)

\(d. 5n^{2}−11n+2=0\)

\(b. (b−4)2<12\)

\(c. ∣3+x∣−9\leq21\)

\(d. 5n^{2}−11n+2=0\)

asked 2021-02-02

Solve the following equations and inequalities for x. Check your solution(s), if possible
\(\displaystyle{a}.{\frac{{{3}}}{{{x}}}}={9}\)

\(\displaystyle{b}.\sqrt{{x}}={4}\)

\(\displaystyle{c}.{x}^{{{2}}}={25}\)

\(\displaystyle{d}.{2}{\left({x}−{3}\right)}{>}{4}\)

\(\displaystyle{b}.\sqrt{{x}}={4}\)

\(\displaystyle{c}.{x}^{{{2}}}={25}\)

\(\displaystyle{d}.{2}{\left({x}−{3}\right)}{>}{4}\)