Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [exponentiation]

Questions about exponentiation, the operation of raising a base $b$ to an exponent $a$ to give $b^a$.

Exponentiation is a mathematical operation which produces a power $a^n$ from a base $a$ and an exponent $n$. The objects involved are usually numbers, but the procedure can be generalized to matrices, elements in algebraic structures, sets, etc.

4326 questions
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Solving for x (multiple x's in the equation)

How would you solve this equation for x. Not sure where to start. Thanks in advance. $$3.5 = (-7e12*x^4) + (-0.9259*x^3) + (7.222*x^2) + (-22.054*x) + 19.757$$
Paul
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Recursive Exponents $s^{(s-1)^{(s-2)^{...(0)}}}$

for $1 \leq S \leq 10^9$ I need $S^{(S-1)^{(s-2)^{...^{1}}}} \mod{n}$ and there must be a way which a program written based on that returns the result for $S = 10^9$ in less than a second. what is the efficient answer?
Ebrahim Tahernejad
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how can I rearrange this formula involving an exponential?

I have this equation $p = r^l$ I know $p$ and $r$ and I would like to solve for $l$, how can I rearrange this formula to achieve this? I initially came up with: $l = \sqrt[r]{p}$ ( $l$ is the $r$th root of $p$) but my intuition says this is wrong…
the_velour_fog
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How many digits are in the decimal representation of $\frac{2^{2001}5^{1950}}{4^{27}}$?

My answer is 1950, but the answer sheet says 1949. I think the answer sheet is wrong. How many digits are in the value of the following expression: $(2^{2001}*5^{1950})/4^{27}$? I solve this problem as following:…
math
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Simplifying indices with surds

I am asked to simplify $(\sqrt{t^3}) \times (\sqrt{t^5})$. I get up to $\sqrt[3]{t^3}\times \sqrt{t^5}$ but I am not sure how to simplify this further as now roots are involved and not just powers. When I checked the solutions the final answer…
Dan
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Why is $4^{n+1} -1 = 4^n - 1 + 3 * 4^n$?

I'm learning about proving equations using induction using an online tutorial, but I'm stuck at this step: $$4 * 4^n-1 = 4^n - 1 + 3 * 4^n$$ I don't know how the author turned the $4$ into $3 * 4^n$. I tried to remove the 4 by multiplying with…
Rakete1111
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Reducing the Index and Improper Fractions

I'm trying to do the problem 3√40x^4/y^9. When you try to reduce the index for 40^4, its going to be 4/3. How does the index get reduced into 2x√5x? I understand 3 cubed of 40, but what happens to the 4/3
CrewdNBasic
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Solve exponential equation under some conditions

Let $a, b, c$ be strictly positive real numbers. Solve the equation $2a^x = b^x + c^x$, given that $c = \sqrt{ab}$. Knowing that $c = \sqrt{ab}$, we get $c^x = \frac{1}{a^xb^x}$. By plugging this in the equation, we get $a^xb^x(2a^x - b^x) =…
George R.
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Weird result from applying power rule of logarithm

I was working on a integration problem involving $3^u$ and noticed something weird. If you assign the value $x = e^3$ then you have that $3^u = ln x^u$. This is also equal to $ulnx$. Heres the weird part $ulnx = u lne^3 = 3u$. I cant find any…
Ziad Fakhoury
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Find zero of this exponential equation

I know that you can find numerically answer to this, but is it possible to express x somehow algebraically $e^{\frac{2}{x}}=x$?
user354021
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How to get to the powers

Consider: $(a + b + c + d)^{21}$ What will be the coefficient of $a^5b^6c^5d^5$? Can you also give the general way of finding out coefficients of such terms?
crimsonKnight
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How do I simplify $6 \cdot 9^{\frac{3x-1} 2}$ into $a \cdot b^x$?

How do I simplify $6 \cdot 9^{\tfrac{3x-1} 2}$ into $a \cdot b^x$? I've been unable to understand how so far. Thanks.
highlandertf2
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Why n and what does it mean?

Maybe a bit too early to ask, but I give it a shot. I'm trying to study mathematics again during my free time. Now I tried to figure out what exactly is meant with the multiple. Well this formula makes it quite easy to understand for me, but it's…
Erik van de Ven
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How can I round up to the nearest power of a number?

I'm sorry if I got the terminology wrong. Let me explain with an example. Given a multiplier (we'll say 2.5), I need an equation or algorithm to find what power level a number resides in (preferably calculated, not a loop). Level 0: < 2.5 Level 1: <…
DaiBu
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finding $x$ when it is the power in both the numerator and denominator

I have an equation and I've simplified it to this: $$\frac {24}{19}=\frac {1.01583^{12x}}{1.01583^{12x}-1}$$ I'm having trouble finding $x$? I realize I have to find the log at some point, but am struggling as to when and where I do so?
Arizona Lee
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