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3 years ago

14

What is the place the 8 is in in the number 38,341,097.54

1 answer:

Sophie [7]3 years ago

4 0

It’s in the Millions place

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Solve the following equations.<br> log2(x^2 − 16) − log^2(x − 4) = 1

Alenkasestr [34]

Answer:

$x=\frac{4*(2+e)}{e-2}$

Step-by-step explanation:

Let's rewrite the left side keeping in mind the next propierties:

$log(\frac{1}{x} )=-log(x)$

$log(x*y)=log(x)+log(y)$

Therefore:

$log(2*(x^{2} -16))+log(\frac{1}{(x-4)^{2} })=1\\ log(\frac{2*(x^{2} -16)}{(x-4)^{2}})=1$

Now, cancel logarithms by taking exp of both sides:

$e^{log(\frac{2*(x^{2} -16)}{(x-4)^{2}})} =e^{1} \\\frac{2*(x^{2} -16)}{(x-4)^{2}}=e$

Multiply both sides by $(x-4)^{2}$ and using distributive propierty:

$2x^{2} -32=16e-8ex+ex^{2}$

Substract $16e-8ex+ex^{2}$ from both sides and factoring:

$-(x-4)*(-8-4e-2x+ex)=0$

Multiply both sides by -1:

$(x-4)*(-8-4e-2x+ex)=0$

Split into two equations:

$x-4=0\hspace{3}or\hspace{3}-8-4e-2x+ex=0$

Solving for $x-4=0$

Add 4 to both sides:

$x=4$

Solving for $-8-4e-2x+ex=0$

Collect in terms of x and add $4e+8$ to both sides:

$x(e-2)=4e+8$

Divide both sides by e-2:

$x=\frac{4*(2+e)}{e-2}$

The solutions are:

$x=4\hspace{3}or\hspace{3}x=\frac{4*(2+e)}{e-2}$

If we evaluate x=4 in the original equation:

$log(0)-log(0)=1$

This is an absurd because log (x) is undefined for $x\leq 0$

If we evaluate $x=\frac{4*(2+e)}{e-2}$ in the original equation:

$log(2*((\frac{4e+8}{e-2})^2-16))-log((\frac{4e+8}{e-2}-4)^2)=1$

Which is correct, therefore the solution is:

$x=\frac{4*(2+e)}{e-2}$

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4 years ago

What expression has a value greater then 4 with the exponet 3

Dmitriy789 [7]

Answer:

5^3

Step-by-step explanation:

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3 years ago

Alyssa bought 5 bags of pretzels and a case of water for $16. The case of water was on sale for $3. How much was each bag of pre

AlekseyPX

The answer is $2.6 dollars

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3 years ago

A prism is completely filled with 96 cubes that have edge length of 12 cm. What is the volume of the prism? Enter your answer in

Anika [276]

Keeping in mind that a cube is just a rectangular prism with all equal sides, so if a side is say "s" units long, the volume of the cube is just s*s*s, or s³.

we know this cubes have a side of 12, thus each one has a volume of 12³, and since we know there are 96 of them, their total volume will just be 96 * 12³, and that'd be the volume of the prism with them.

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3 years ago

Read 2 more answers

Can someone please help me out

Oksi-84 [34.3K]

Answer:

A/ 0

B/ 6

C/

$3 {x}^{2} + 6x - 18$

D/ 77

E/ 33

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3 years ago