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hichkok12 [17]
3 years ago
13

3 to the power 2x+3 is subtracted by 9 which is equal to 2 times 9 to the power x+1 and is subtrcted by 6

Mathematics
1 answer:
hichkok12 [17]3 years ago
5 0

Answer:

x = -0.5

Step-by-step explanation:

Here we have the sentence:

"3 to the power 2x+3 is subtracted by 9 which is equal to 2 times 9 to the power x+1 and is subtracted by 6"

The first part:

"3 to the power 2x+3 is subtracted by 9..."

This can be written as:

3^{2x + 3} - 9

"... is equal to 2 times 9 to the power x+1 and is subtracted by 6"

3^{2x + 3} - 9 = 2*9^{x + 1} - 6

Let's solve this for x.

First, we can add 9 in both sides:

3^{2x + 3}  = 2*9^{x + 1} - 6 + 9 =  2*9^{x + 1} + 3

We also know the relations:

a^n*a^b = a^{n + b}

and

(a^n)^m = a^{n*m}

We can write the left part as:

3^{2x + 3} = 3^{2x}*3^3 = (3^2)^x*3^3 = 9^x*27

And the right side as:

2*9^{x + 1} + 3 = 2*9^x*9 + 3 = 18*9^x + 3

Then the equation becomes:

27*9^x = 18*9^x + 3

Now let's move both terms with 9^x to the left side:

27*9^x - 18*9^x = 3\\

(27 - 18)*9^x = 3

9*9^x = 3

9^x = 3/9 = 1/3

Now remember that:

Ln(a^b) = b*Ln(a)

Then if we apply the Ln( ) function to both sides, we get:

Ln(9^x) = Ln(1/3)

x*Ln(9) = Ln(1/3)

x = \frac{Ln(1/3)}{Ln(9)} = -0.5

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3 years ago
Given the equation −4x + 10 = 2, which order of operations completely solves for x?
hammer [34]
Hi there!

Answer:
The answer is "<span>Subtract 10, then divide by −4"

Explanation:
To solve a linear equation (for x) we need to isolate the variable (x). First we need to bring the variables to the left side (in this case, it is already on the correct place). Next up is bringing all the integers to the right side. Therefore, we must first subtract 10. Our final step is dividing by the number that is placed in front of x (in this case divide by </span><span>−4)
</span><span>
Solving the equation:
</span><span>−4x + 10 = 2
First subtract 10 (from both sides of the equation)

</span>−4x  = −8
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