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I assume we have

log₁₆ 19     using the "change of base" rule we have

log19/log16 = about 1.062

I would disagree that 0^0 = 1.

I believe that it is an indeterminate expression; which means that it can have any value, depending upon how it was created.

I do fully agree that a^0 = 1, whenever a ≠ 0.

Very nice !!!!....you're not as "limited" as you think !!!!

I repeat!

I just worked out a.   you have to multiply top and bottom by the conjugate of the top and then it just falls out. 

It is quite simple this way.  :)

$$\displaystyle\lim_{x\rightarrow 0} \frac{\sqrt{2x+4}-2}{x}\\\\
=\displaystyle\lim_{x\rightarrow 0} \frac{\sqrt{2x+4}-2}{x}\times \frac{\sqrt{2x+4}+2}{\sqrt{2x+4}+2}\\\\
=\displaystyle\lim_{x\rightarrow 0} \frac{(2x+4)-4}{x(\sqrt{2x+4}+2)}\\\\
=\displaystyle\lim_{x\rightarrow 0} \frac{2}{(\sqrt{2x+4}+2)}\\\\
=\frac{2}{(\sqrt{2*0+4}+2)}\\\\
=\frac{2}{4}\\\\
=\frac{1}{2}$$

1. 3x^(2/3)+4x^(1/3)-4=0    I re-wrote this to what I think you meant

Factoring directly, we have

(3x^(1/3) - 2) (x^(1/3) + 2) = 0

Setting each factor to 0, we have

3x^(1/3) - 2 =0   add 2 to both sides

3x^(1/3) = 2    divide by 3 on both sides

x^(1/3) = 2/3   cube both sides

x = 8/27

And for the other factor, we have

x^(1/3) + 2 = 0

Subtract 2 from both sides

x^(1/3) = -2   cube both sides

x = -8

2. (1+1/x)^2 - 6(1+1/x) + 8 =0

We can factor this directly, too

[(1 + 1/x) - 4] [(1 + 1/x) - 2] = 0

Set each factor to 0

(1 + 1/x) - 4 = 0   add 4 to both sides

1 + 1/x = 4          subtract 1 from both sides

1/x = 3               divide by 3 and multiply by x on both sides

x = 1/3

And for the other factor, we have

(1 + 1/x) - 2 = 0   add 2 to both sides

1 + 1/x = 2    subtract 1 from both sides

1/x = 1          so x = 1

$$\\\frac{5^7}{5^7}=5^{7-7}=5^0\\\\
$but$\\\\
$any non-zero number divided by itself $\\\\
so\\\\
5^0=1\\\\
$Anything (including 0) raised to the 0 power is 1 $$$

11^2=121

so 

x=11 or x=-11

Hi youngzone,

Whatever happened to 'please'.    Plus, I think that your pirst expression is missing and x

If 1/3=33.3 repeater %

And 2/3=66.6 repeater %

Would 3/3 be 99.9 repeater % or 100%?

$$\\0.\dot3 = 1/3\\
0.\dot6 = 2/3\\
0.\dot9 = 3/3 = 1\\\\
$that is $\\
0.\dot9 \;=\; 99.\dot9\%\; =\; 1\\\\
$They really are equal! $$$

|-8-3|=|-11|=11

Absolute value is just the distance from 0 on the number line. 

so negative numbers become positive and positive numbers stay positive.  

the answer is 19

3/3 = 1 or 100% ...... The values for 1/3 and 2/3 are decimal approximations.

3.1415926535897932384626433832795028841971693993751058209

That's all I remember.

Pi is equal to the circumference of a circle divided by its diameter.

Please, be friendly to one another. Use appropriate language as this is an educational tool, often used by students. Thank you.

We can actually use a trick here to factor this as a sum of cubes.

x^4 + y^6   =  (x^4/3)^3 + (y^2)^3....so we have

[x^(4/3) + y^(2)] [x^(8/3) - x^(4/3)y^(2) + y^(4)]

However, the first term could also be factored as a sum of cubes......and we could probably continue this process forever!!!!

Yes, the quotient is 84 and the remainder is 8.

If you use a calculator to divide 764 by 9 and get an answer like 84.8888888889 (the number in front of the decimal point, the 84, give you the quotient) and you want to find the remainder, do this:

first, subtract the number in fromt of the decimal point; subtract the 84, and you will have .8888888889 on your calculator;

then mulitply this long decimal by your original divisor (the 9); now, the answer on your calculator will be the remainder.

Example:  find the quotient and remainder of 86 divided by 7.

Divide 86 by 7:  12.28571429      --->  the quotient is 12

Subtract the 12:  .2857142857

Multiply by 7:  2                           --->  the remainder is 2

Well, first you should finish up the calculations within the brackets:

6=a(1-5)(1+3)  becomes  6=a(-4)(4)

Then, simplify by multiplying the bracketed number together:

6=a(-4)(4) becomes 6=a(-16)

Finally, divide -16 from both sides to isolate a:

6=a(-16) becomes 6/-16=(a*-16)/-16, the -16's on the right side cancel

to leave a isolated and equal to 6/-16 or -3/8 or -0.375, and yer done!

This is not an equation; to have an equation, you have to have an equal sign and something on the other side.

"at least" becomes "≥".

"fewer than" means subtract, so "9 fewer than" becomes "- 9".

y represents the pages read on Saturday.

x represents the pages read on Friday.

y  ≥  4x - 9

Draw the line y = 4x -9 and shade the region above the line to show "at least".

Points that you can use:  x = 0 and y = -9                  x = 4 and y = 7.

Do you have to be more careful than this? Because, x can't be negative and y can't be negative (you can't read a negative number of pages); do you have to worry about this?

One method is to just select a value for x and substitue it into the equation to  find y.

Then, select another value for x and substitute that into the equation to find a second y.

Plot both points on a graph and draw a line between them.

Hint.... ( I might use 0 and 1 for the two x values to substitute)....post back if you have trouble

Since there is no x-term on the right side of the function, any value of x can be used to make f(x) = 12/16.

In fact, there is no way to make f(x) have any value but 12/16.

For instance:  f(0) = 12/16, and f(1) = 12/16, and f(2.75) = 12/16, etc., for all values of x.

6 = a(1-5)(1+3)    simplify

6 = a(-4)(4)

6 = a (-16)     divide both sides by -16

-6/16 = a = -3/8

the sixteenth letter of the Greek alphabet ( Π, π ), transliterated as ‘p

the numerical value of the ratio of the circumference of a circle to its diameter (approximately 3.14159).