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3 years ago

The log of x cubed times y squared simplified

Mathematics

1 answer:

tresset_1 [31]3 years ago

4 0

Answer:

$log(x^{3}y^{2}) = 3 log x+2 log y$

Step-by-step explanation:

Step 1:-

using logarithmic formula $log(ab)=log a+log b$

so given $log(x^{3} y^{2} ) = log (x^{3} )+log(y^{2} )$

now simplify

= $3 log x+2 log y$

<u>Answer:</u>-

$log(x^{3}y^{2})= [tex]3 log x+2 log y$

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sammy [17]

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3 years ago

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2 years ago

Write the slope-intercept form equation of the line that passes through (1,-1) and (2, 2).

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Answer:

The answer to your question is y= 3x - 4.

Step-by-step explanation:

Plot the points (1,-1) and (2,2) and get your slope, in the case of slope-intercept form "m" using the rise/run method. You rise 3 units and run one unit to the right to get from (1,-1) to (2,2), so your slope is 3/1 or just simply 3. -4 is your y-intercept, or "b", because if you plot the two aforementioned points (1,-1) and (2,2) and make a line with them, your line meets the y-axis at the point (0, -4). Hope this helps!

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3 years ago

Consider the following sets of matrices: M2(R) is the set of all 2 x 2 real matrices; GL2(R) is the subset of M2(R) with non-zer

defon

Answer:

Step-by-step explanation:

REcall the following definition of induced operation.

Let * be a binary operation over a set S and H a subset of S. If for every a,b elements in H it happens that a*b is also in H, then the binary operation that is obtained by restricting * to H is called the induced operation.

So, according to this definition, we must show that given two matrices of the specific subset, the product is also in the subset.

For this problem, recall this property of the determinant. Given A,B matrices in Mn(R) then det(AB) = det(A)*det(B).

Case SL2(R):

Let A,B matrices in SL2(R). Then, det(A) and det(B) is different from zero. So

$\text{det(AB)} = \text{det}(A)\text{det}(B)\neq 0$ .

So AB is also in SL2(R).

Case GL2(R):

Let A,B matrices in GL2(R). Then, det(A)= det(B)=1 is different from zero. So

$\text{det(AB)} = \text{det}(A)\text{det}(B)=1\cdot 1 = 1$ .

So AB is also in GL2(R).

With these, we have proved that the matrix multiplication over SL2(R) and GL2(R) is an induced operation from the matrix multiplication over M2(R).

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3 years ago

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Answer:

Step-by-step explanation:

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