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3 years ago

What is the solution to the equation below?

Mathematics

1 answer:

lara31 [8.8K]3 years ago

8 0

Answer:

$x=4096$ , Option B

Step-by-step explanation:

Given, $\log_{8}x=4$

Formula needed,

$\log_{a}b=\frac{\log b}{\log a}$

Therefore,

$\log_{8}x=\frac{\log x}{\log 8}$

$\frac{\log x}{\log 8}=4$

${\log x}=4{\log 8}$

$\log x={\log 8^4}$

$x=8^4$

$x=4096$

Option B is correct.

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IgorLugansk [536]

The graph of $\mathbf{y=\sin{3x}}$ is given by,

Here given the function is $y=\sin{3x}$

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When $x=\frac{\pi}{6}\Rightarrow y=\sin{3\times\frac{\pi}{6}}=\sin\frac{\pi}{2}=1$

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2 years ago

How many times greater is 9*10^10 than 3*10^8

vladimir2022 [97]

Answer:

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Step-by-step explanation:

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3 years ago

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Step-by-step explanation:

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3 years ago

Stans steak house has a server to cook ratio of 5 to 2.The total number of servers and cooks is 42. How many servers does Stans

aivan3 [116]

Answer: 30 servers

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Step-by-step explanation:

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3 years ago

Factor the polynomial, x2 + 5x + 6

patriot [66]

Answer:

Choice b.

$x^{2} + 5\, x + 6 = (x + 3)\, (x + 2)$ .

Step-by-step explanation:

The highest power of the variable $x$ in this polynomial is $2$ . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to $0$ .)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to $0$ . The discriminant of this polynomial is $(5^{2} - 4 \times 1 \times 6) = 1$ .

$\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}$ .

Similarly:

$\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}$ .

By the Factor Theorem, if $x = x_{0}$ is a root of a polynomial, then $(x - x_0)$ would be a factor of that polynomial. Note the minus sign between $x$ and $x_{0}$ .

The root $x = -2$ corresponds to the factor $(x - (-2))$ , which simplifies to $(x + 2)$ .
The root $x = -3$ corresponds to the factor $(x - (-3))$ , which simplifies to $(x + 3)$ .

Verify that $(x + 2)\, (x + 3)$ indeed expands to the original polynomial:

$\begin{aligned}& (x + 2)\, (x + 3) \\ =\; & x^{2} + 2\, x + 3\, x + 6 \\ =\; & x^{2} + 5\, x + 6\end{aligned}$ .

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2 years ago