Solve by Radical: xⁿ=c
Read this topicExplanations 3
- (Video) Exponents in Algebra by Math Antics This video by Math Antics shows you how to solve equations in the form xn=cx^n=cxn=c. Summary We solve any algebraic equation by isol…
By Alex Federspiel, Ruiran Xun, Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
- Solving xn=cx^n = cxn=c with prime factorization Suppose ccc is a real number. We want to solve the equation and find the real solutions of xn=cx^n = cxn=c If nnn is odd, then t…
By Christine, Victor Wang, Alex Federspiel, Amy Feraco, Caroline K, Jonathan Heller, Anusha Rahman
- Solve by Radical: xn=cx^{n}=cxn=c This concept can get kind of confusing, so let's think about how we could rewrite the following equation: x=42x = \sqrt[2]{4}x=24 We would sta…
By Eunji Kwon, Jonathan Heller, Caroline K, Anusha Rahman
Problems 33
- The area of a circle is 16π16\pi16π. Use this to find the radius of the circle.
- Solve for the radius of a sphere, rrr, in terms of the volume, VVV. V=43 πr3V=\frac{4}{3}\ \pi r^3V=34 πr3
- Find the common ratio of the geometric sequence with a3=12a_{3} = 12a3=12 and a6=96a_{6} = 96a6=96.
- Find the largest integer nnn for which n200<5300n^{200} < 5^{300}n200<5300. Source: Alex Zhu, Problems of the Week 2, 2012
- How many real solutions does the equation ∣x2−2∣=1|x^2 - 2| = 1∣x2−2∣=1 have?
- How many real solutions does the equation ∣x2−2∣=2|x^2 - 2| = 2∣x2−2∣=2 have?
- How many real solutions does the equation ∣x2−2∣=3|x^2 - 2| = 3∣x2−2∣=3 have?
- The equation for compound interest is A=P(1+rm)tmA=P(1+\frac{r}{m})^{tm}A=P(1+mr)tm. Solve for rrr.
- If x,y,zx,y,zx,y,z are real numbers such that x2y2=8yx=z\frac{x^2}{y^2} = \frac{8y}{x} = zy2x2=x8y=z, what is zzz? Source: Mandelbrot #3
- Solve for xxx. x2=169x^2=169x2=169
- Solve for xxx. x3=64x^3=64x3=64
- Solve for xxx. x3=343x^3=343x3=343
- Solve for xxx. x4=1296x^4=1296x4=1296
- Suppose that a geometric sequence has a5=120a_5 = 120a5=120 and a8=3240a_8 = 3240a8=3240. What is the common ratio of the geometric sequence?
- If 72y=367^{2y} = 3672y=36, compute 7−y7^{-y}7−y. Write your answer as a fraction pq\frac{p}{q}qp in simplest form, with no spaces.
- The diameter of the moon is 215921592159 miles. The volume of Earth is about 49.349.349.3 times larger than that of the moon. What is the Earth's diameter, approximately?
- Solve the inequality: x2≤−3,x∈R.x^2\leq{-3}, x \in \mathbb{R}.x2≤−3,x∈R.
- Solve for the possible real value(s) of xxx. 25x4=20\sqrt{25x^4}=2025x4=20
- 4x6=16\sqrt{4x^6}=164x6=16 Solve for xxx, given that x>0x>0x>0.
- Solve for xxx. x2=9x^2=9x2=9
- Solve for xxx. x3=8x^3=8x3=8
- Solve for xxx. x2=36x^2=36x2=36
- Solve for xxx. x2=64x^2=64x2=64
- Find a way to solve for π\piπ using the formula for volume: V=43πr3V=\frac{4}{3}\pi r^3V=34πr3
- The volume of a cube with side length sss is V=s3V=s^3V=s3. Isolate sss in terms of VVV.
- x3=162x^3 = 162x3=162 Solve for xxx.
- Solve equation (A) and plug the result into expression (B). x3=8(A)x2(B)\begin{array}{lc} x^3=8&\quad\small{(A)}\\ \sqrt{x^2}&\quad\small{(B)} \end{array}x3=8x2(A)(B)
- What is the value of xxx?
- What is the value of xxx?
- What is the value of xxx?
- What is the value of xxx?
- What is the value of xxx?
- What is the value of xxx?