# Questions tagged [algebra-precalculus]

For questions about algebra and precalculus topics, which include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomial, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

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### Translating regular wording into a mathematical expression

Given a product that initially costs $2000$ dollars and will cost $200$ dollars more on each subsequent purchase (for example a total of $6600$ spent on the third purchase), how would I write a ...
81 views

### Solving for x in logarithmic equation $\log_4(2x) = \frac{1}{2}x^2 - 1$

I am trying to solve for $x$ in the equation $\log_4(2x) = \frac{1}{2}x^2 - 1$. I have tried converting the logarithmic expression to exponential form, but I am not able to isolate $x$ in the ...
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On what ground can $1/b$ = $a^{(3b-1)}$ be identified as $b = a^{(1-3b)}$. . Thank you EDIT: To be fully understood, my question is regarding identity. Here is my way, I'm not sure if the following ...
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### Showing that $\sup_{x\in[0,1]}|f(x)|\leq \sqrt{\int_0^1(f'(x))^2dx}$ when $f\in C^1([0,1],\mathbb{R})$ and $f(0) = 0$

Let $f\in C^1([0,1],\mathbb{R})$ such that $f(0) = 0$. I am trying to show that $\sup_{x\in[0,1]}|f(x)|\leq \sqrt{\int_0^1(f'(x))^2dx}$. I have a suspicion that we ought to use the mean value theorem ...
205 views

### Boxes and dice game

You have $9$ boxes numbered $1$ through $9$ and then you have two $6$-sided dice. Each turn you roll the two dice and deduct the sum of the dice from the boxes by removing the number itself or any ...
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The problem is somewhat tricky. I would like to generate a set of number pairs $(x_1, y_1), (x_2, y_2)...$ so that each pair of numbers has uniqueness on all four computations (addition, subtraction, ...
Can you tell me what is wrong of my solution that is not found in possible answers which are $1, {{5}{/}{2}}, \sqrt{2}, 2, 3$  \text { if } \quad x+\frac{2}{\sqrt{x}}=5 \quad \text {, what is} \...