Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- log(1/3,(4-x)(x^2+29))<=log(1/3,(x^2-10x+24)(7-x))
-
45^(x)-27^x-18*15^x+2*9^(x+1)+81*5^x-3^(x+4)<=0
- x^2-29x<0
- ((15^x-3^(x+1)-5^(x+1)+15)*1/(-x^2+2*x))>=0
-
Identical expressions
- log(one / three ,(four -x)(x^ two + twenty-nine))<=log(one / three ,(x^ two -10x+ twenty-four)(seven -x))
- logarithm of (1 divide by 3,(4 minus x)(x squared plus 29)) less than or equal to logarithm of (1 divide by 3,(x squared minus 10x plus 24)(7 minus x))
- logarithm of (one divide by three ,(four minus x)(x to the power of two plus twenty minus nine)) less than or equal to logarithm of (one divide by three ,(x to the power of two minus 10x plus twenty minus four)(seven minus x))
- log(1/3,(4-x)(x2+29))<=log(1/3,(x2-10x+24)(7-x))
- log1/3,4-xx2+29<=log1/3,x2-10x+247-x
- log(1/3,(4-x)(x²+29))<=log(1/3,(x²-10x+24)(7-x))
- log(1/3,(4-x)(x to the power of 2+29))<=log(1/3,(x to the power of 2-10x+24)(7-x))
- log1/3,4-xx^2+29<=log1/3,x^2-10x+247-x
- log(1 divide by 3,(4-x)(x^2+29))<=log(1 divide by 3,(x^2-10x+24)(7-x))
-
Similar expressions
- log(1/3,(4-x)(x^2+29))<=log(1/3,(x^2-10x+24)(7+x))
- log(1/3,(4-x)(x^2+29))<=log(1/3,(x^2-10x-24)(7-x))
- log(1/3,(4-x)(x^2-29))<=log(1/3,(x^2-10x+24)(7-x))
- log(1/3,(4-x)(x^2+29))<=log(1/3,(x^2+10x+24)(7-x))
- log(1/3,(4+x)(x^2+29))<=log(1/3,(x^2-10x+24)(7-x))
log(1/3,(4-x)(x^2+29))<=log(1/3,(x^2-10x+24)(7-x)) inequation
The solution
You have entered
[src]
/ / 2 \\ / / 2 \ \ log\1/3, (4 - x)*\x + 29// <= log\1/3, \x - 10*x + 24/*(7 - x)/
$$\log{\left(\frac{1}{3} \right)} \leq \log{\left(\frac{1}{3} \right)}$$
log(1/3, (4 - x)*(x^2 + 29)) <= log(1/3, (7 - x)*(x^2 - 10*x + 24))
Detail solution
Given the inequality:
$$\log{\left(\frac{1}{3} \right)} \leq \log{\left(\frac{1}{3} \right)}$$
To solve this inequality, we must first solve the corresponding equation:
$$\log{\left(\frac{1}{3} \right)} = \log{\left(\frac{1}{3} \right)}$$
Solve:
$$x_{1} = 1$$
$$x_{1} = 1$$
This roots
$$x_{1} = 1$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 1$$
=
$$\frac{9}{10}$$
substitute to the expression
$$\log{\left(\frac{1}{3} \right)} \leq \log{\left(\frac{1}{3} \right)}$$
$$\log{\left(\frac{1}{3} \right)} \leq \log{\left(\frac{1}{3} \right)}$$
the solution of our inequality is:
$$x \leq 1$$
$$\log{\left(\frac{1}{3} \right)} \leq \log{\left(\frac{1}{3} \right)}$$
To solve this inequality, we must first solve the corresponding equation:
$$\log{\left(\frac{1}{3} \right)} = \log{\left(\frac{1}{3} \right)}$$
Solve:
$$x_{1} = 1$$
$$x_{1} = 1$$
This roots
$$x_{1} = 1$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 1$$
=
$$\frac{9}{10}$$
substitute to the expression
$$\log{\left(\frac{1}{3} \right)} \leq \log{\left(\frac{1}{3} \right)}$$
$$\log{\left(\frac{1}{3} \right)} \leq \log{\left(\frac{1}{3} \right)}$$
-log(3) -log(3) ---------- ---------- /92411\ <= /96441\ log|-----| log|-----| \ 1000/ \ 1000/
the solution of our inequality is:
$$x \leq 1$$
_____
\
-------•-------
x_1
Solving inequality on a graph
Rapid solution
[src]
/ / _______________ \ \ | | / ____ | | | | ___________________ / 47 3*\/ 93 | | | | / ________ 3 / -- + -------- | | | | 4 / 2189 \/ 691485 71 17 7 \/ 2 2 | | Or|And|x < - + 3 / ---- + ---------- - --------------------------, -- - ---------------------- - -------------------- < x|, x <= 1| | | 3 \/ 54 18 ___________________ 3 _______________ 3 | | | | / ________ / ____ | | | | / 2189 \/ 691485 / 47 3*\/ 93 | | | | 9*3 / ---- + ---------- 3*3 / -- + -------- | | \ \ \/ 54 18 \/ 2 2 / /
$$\left(x < - \frac{71}{9 \sqrt[3]{\frac{2189}{54} + \frac{\sqrt{691485}}{18}}} + \frac{4}{3} + \sqrt[3]{\frac{2189}{54} + \frac{\sqrt{691485}}{18}} \wedge - \frac{\sqrt[3]{\frac{3 \sqrt{93}}{2} + \frac{47}{2}}}{3} - \frac{7}{3 \sqrt[3]{\frac{3 \sqrt{93}}{2} + \frac{47}{2}}} + \frac{17}{3} < x\right) \vee x \leq 1$$
(x <= 1)∨((x < 4/3 + (2189/54 + sqrt(691485)/18)^(1/3) - 71/(9*(2189/54 + sqrt(691485)/18)^(1/3)))∧(17/3 - 7/(3*(47/2 + 3*sqrt(93)/2)^(1/3)) - (47/2 + 3*sqrt(93)/2)^(1/3)/3 < x))
Rapid solution 2
[src]
_______________ _____________________
3 ___ 2/3 3 / ____ 3 ___ 2/3 3 / ________
17 7*\/ 2 2 *\/ 47 + 3*\/ 93 4 71*\/ 2 2 *\/ 2189 + 3*\/ 691485
(-oo, 1] U (-- - -------------------- - -----------------------, - - -------------------------- + -----------------------------)
3 _______________ 6 3 _____________________ 6
3 / ____ 3 / ________
3*\/ 47 + 3*\/ 93 3*\/ 2189 + 3*\/ 691485
$$x\ in\ \left(-\infty, 1\right] \cup \left(- \frac{2^{\frac{2}{3}} \sqrt[3]{3 \sqrt{93} + 47}}{6} - \frac{7 \cdot \sqrt[3]{2}}{3 \sqrt[3]{3 \sqrt{93} + 47}} + \frac{17}{3}, - \frac{71 \cdot \sqrt[3]{2}}{3 \sqrt[3]{2189 + 3 \sqrt{691485}}} + \frac{4}{3} + \frac{2^{\frac{2}{3}} \sqrt[3]{2189 + 3 \sqrt{691485}}}{6}\right)$$
x in Union(Interval(-oo, 1), Interval.open(-2^(2/3)*(3*sqrt(93) + 47)^(1/3)/6 - 7*2^(1/3)/(3*(3*sqrt(93) + 47)^(1/3)) + 17/3, -71*2^(1/3)/(3*(2189 + 3*sqrt(691485))^(1/3)) + 4/3 + 2^(2/3)*(2189 + 3*sqrt(691485))^(1/3)/6))