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kirill115 [55]
2 years ago
9

Solve for x 64^x^2 = 256^x

Mathematics
1 answer:
kifflom [539]2 years ago
8 0

Answer:

x = 0, 1.333333...

Step-by-step explanation:

1) Convert both sides to the same base.

16^{1.5x^{2} } =16^{2x}

2) Cancel the base of 16  on both sides.

1.5x^{2} =2x

3) Move all terms to one side.

1.5x^{2} -2x=0

4) Factor out the common term x.

x(1.5x-2)=0

5) Solve for x.

1 - Ask: When will x(1.5x-2) equal zero?

When x = 0 or 1.5x - 2 = 0
2 - Solve each of the 2 equations above.

x = 0, 1.333333...

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Find all solutions by transforming the system to reduced echelon form and back substituting. (If there are an infinite number of
Zolol [24]

Answer:

The system has infinite solutions described in the set \{(x_1,x_2,x_3)=(6+s1, -10-2s1,s1): s1\in\mathbb{R}\}

Step-by-step explanation:

The augmented matrix of the system is \left[\begin{array}{cccc}-1&-1&-1&4\\2&1&0&2\end{array}\right].

We apply row operations:

1. We add the first row to the second row twice and obtain the matrix \left[\begin{array}{cccc}-1&-1&-1&4\\0&-1&-2&10\end{array}\right]

2. multiply by -1 the rows of the previous matrix and obtain the matrix \left[\begin{array}{cccc}1&1&1&-4\\0&1&2&-10\end{array}\right] that is the reduced echelon form of the matrix associated to the system.

Now we aply backward substitution:

1. Observe that the reduced echelon form has a free variable, then the system has infinite solutions.

2.

x_2+2x_3=-10\\x_2=-10-2x_3

3.

x_1+x_2+x_3=-4\\x_1-10-2x_3+x_3=-4\\x_1-x_3=-4+10\\x_1=6+x_3.

Then the set of solutions is \{(x_1,x_2,x_3)=(6+s1, -10-2s1,s1): s1\in\mathbb{R}\}

3 0
3 years ago
-3/7 x -3/7 = what ? please help
Snowcat [4.5K]

Answer:

9/49 is the answer

Step-by-step explanation:

3 0
3 years ago
In the figure below, AD is the perpendicular bisector of CB. Based on this information, which other statement can be proven to b
snow_tiger [21]

Answer:

463833

expand

Medium

Solution

verified

Verified by Toppr

In △ABD and △ACD, we have

DB=DC ∣ Given

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AD=AD ∣ Common

∴ by SAS criterion of congruence, we have.

△ABD≅△ACD

⇒AB=AC ∣ Since corresponding parts of congruent triangles are equal

Hence, △ ABC is isosceles.

5 0
2 years ago
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Katyanochek1 [597]
Sorry don’t know but good luck
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Answer:

1/10th?

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