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miss Akunina [59]
3 years ago
8

Please help :)

Mathematics
1 answer:
olga nikolaevna [1]3 years ago
3 0
The answer is linear pair postulate hope this helps.❤️
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H(x) = 2^x<br>Solve the equation h^-1 (x) =0.5​
Ludmilka [50]

Answer:

The answer is

<h2>\sqrt{2}  \:  \: or \:  \: 1.414</h2>

Step-by-step explanation:

<h3>h(x) =  {2}^{x}</h3>

To solve the equation we must first find h-¹(x)

To find h-¹(x) equate h(x) to y

That's

<h3>y =  {2}^{x}</h3>

<u>Next interchange the terms </u>

x becomes y and y becomes x

That's

<h3>{2}^{y}  = x</h3>

<u>Make y the subject</u>

Take logarithm to base 2 to both sides

That's

<h3>log_{2}( {2} )^{y}  =  log_{2}x \\ y  log_{2}2 =  log_{2}(x)</h3>

But

<h3>log_{2}(2)  = 1</h3><h3>y =  log_{2}(x)</h3>

So we have

<h3>{h}^{ - 1} (x) =  log_{2}(x)</h3>

Now we can solve the equation

We have

<h3>log_{2}(x)  = 0.5</h3>

Convert the logarithm into exponential form using the fact that

<h3>log_{a}(x)  = b \:  \:  \cong \:  \: x =  {a}^{b}</h3>

So we have

<h3>x =  {2}^{0.5}</h3>

But

<h3>{2}^{0.5}  =  \sqrt{2}</h3>

So we have the final answer as

<h3>\sqrt{2}  \:  \: or \:  \: 1.414</h3>

Hope this helps you

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67 is an odd number.

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