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1 year ago

If x^y = z is there any way to find y if you know x and z?

Mathematics

1 answer:

Rzqust [24]1 year ago

6 0

We make use of $y = \log_x(z)$ to solve for y, when you know x and z

<h3>How to solve for y?</h3>

The expression is given as:

x^y = z

The above expression is an exponential expression.

Start by taking the logarithm of both sides

y log(x) = log(z)

Divide both sides by log(x)

$y = \log_x(z)$

Hence, we make use of $y = \log_x(z)$ to solve for y, when you know x and z

Read more about exponential functions at:

brainly.com/question/11464095

#SPJ1

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Calculate the pH of a buffer solution made by mixing 300 mL of 0.2 M acetic acid, CH3COOH, and 200 mL of 0.3 M of its salt sodiu

Lesechka [4]

Answer:

Approximately $4.75$ .

Step-by-step explanation:

Remark: this approach make use of the fact that in the original solution, the concentration of $\rm CH_3COOH$ and $\rm CH_3COO^{-}$ are equal.

${\rm CH_3COOH} \rightleftharpoons {\rm CH_3COO^{-}} + {\rm H^{+}}$

Since $\rm CH_3COONa$ is a salt soluble in water. Once in water, it would readily ionize to give $\rm CH_3COO^{-}$ and $\rm Na^{+}$ ions.

Assume that the $\rm CH_3COOH$ and $\rm CH_3COO^{-}$ ions in this solution did not disintegrate at all. The solution would contain:

$0.3\; \rm L \times 0.2\; \rm mol \cdot L^{-1} = 0.06\; \rm mol$ of $\rm CH_3COOH$ , and

$0.06\; \rm mol$ of $\rm CH_3COO^{-}$ from $0.2\; \rm L \times 0.3\; \rm mol \cdot L^{-1} = 0.06\; \rm mol$ of $\rm CH_3COONa$ .

Accordingly, the concentration of $\rm CH_3COOH$ and $\rm CH_3COO^{-}$ would be:

$\begin{aligned} & c({\rm CH_3COOH}) \\ &= \frac{n({\rm CH_3COOH})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}$ .

$\begin{aligned} & c({\rm CH_3COO^{-}}) \\ &= \frac{n({\rm CH_3COO^{-}})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}$ .

In other words, in this buffer solution, the initial concentration of the weak acid $\rm CH_3COOH$ is the same as that of its conjugate base, $\rm CH_3COO^{-}$ .

Hence, once in equilibrium, the $\rm pH$ of this buffer solution would be the same as the ${\rm pK}_{a}$ of $\rm CH_3COOH$ .

Calculate the ${\rm pK}_{a}$ of $\rm CH_3COOH$ from its ${\rm K}_{a}$ :

$\begin{aligned} & {\rm pH}(\text{solution}) \\ &= {\rm pK}_{a} \\ &= -\log_{10}({\rm K}_{a}) \\ &= -\log_{10} (1.76 \times 10^{-5}) \\ &\approx 4.75\end{aligned}$ .

7 0

2 years ago

Today, the mailman sorted 57 letters during his first hour of work, 69 letters during his second hour, 81 letters during his thi

mars1129 [50]

The answer is 93

If we sorted out the number of each hours, the sequence will look like this

57 _ 69 _ 81 _ x _ 105

(in which x is the fourth hour of work)

We can see from the sequence that each hours, the mailman add additional 12 letters.
(69 - 57 = 12)
(81 - 69 = 12) . . . . proof

So, the amount of letters on the fourth hour would be:
81 letters + 12 letters = 93 Letters

5 0

3 years ago

Find the missing coefficient. -___________ y2 − [-5y − y(-7y − 9)] − [-y (15y + 4)] = 0

Luden [163]

y = 0
Hope this helps! (:

7 0

3 years ago

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PLEASE HELP ME THANK YOU!

krok68 [10]

You would have to watch 62 3D movies to make an annual pass the less expensive option out of the two of them.

62x25 = 1550

4 0

3 years ago

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a group of 25 sixth graders, 40% of them said they had never visited another state. How many students said they had never visite

diamong [38]

Correct Answer: 10 students have never visited another state
40/100 × 25 =
40 is out of 100 because percentages always is represented by 100 (cent)

cross out the zero's equally top and bottom
so it would become: 4/100 × 25 = 4 ×25 = 100
then add the denominator
100/10 is our final resolution

cross out the zeros evenly and answer will give you 10.

6 0

3 years ago

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