geno3141

Generally speaking, if the variable is in the exponent, use logs (either common logs or natural logs):

3^{x - 1}  =  24

Take the log of both sides:

log(3^{x - 1})  =  log(24)

The reason that logs are used is that the exponent within a logarithm comes out as a multiplier:

(x - 1)log(3)  =  log(24)

Now, divide both sides by the log(3):

x - 1  =  log(24) / log(3)                        If you want, simplify this by using a calculator ...

And, add 1 to both sides:

x  =  log(24) / log(3) + 1                       If you haven't used a calculator yet, use one now ...

(-rs)(rs³)²                                  With an exponent raised to an exponent, multiply the exponents:

=  (-rs)(r²s⁶)                       When mulitplying variables with exponents, add the exponents:

=  -r³s⁷

They are not exactly the same. They will have the same value for all values for x except -3.

If x = -3, then x + 2 = 1, but ((x+2)(x+3))/(x+3) is undefined because it a denominator of zero, and division by zero is undefined.

8x/3 - 2x/4  =  -13

Multiply both sides by the lowest common denominator, 12:

12(8x/3) - 12(2x/4)  =  12(-13)

32x - 6x  =  -156

26x  =  -156

x  =  -6

sin(2x)  =  2sin(x)cos(x)

Since  sin(x)cos(x)  =  0.37115,  2sin(x)cos(x)  =  0.7423.

Therefore,  sin(2x)  =  0.7423.

--->   2x  =  sin^-1(0.7423)

--->   2x  =  49.9277°

--->     x  =  23.96°

Try this:  

Label one die with the numbers:          2, 4, 6, 8, 10, and 12.

Label the other die with the numbers: -1, -1, -1, 0, 0, and 0.

When the second die shows a -1, the sum of the two dice will be 1, 3, 5, 7, 9, or 11.

When the second die shows a 0, the sum of the two dice will be 2, 4, 6, 8, 10, or 12.

Since there is an equal chance for the first second die to show a -1 or a 0,

there will be equal chances for the two dice to sum to 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12.

(k - 1) / 5  =  12

First:  multiply both sides by 5:

--->   5 · (k - 1) / 5  =  12 · 5

--->   k - 1  =  60

Now, add 1 to both sides:

--->   k  =  61

A bar notation means one of two things:

1)  If you have 7.263 with a bar above the 63:  this means that the 63 is repeated forever; 7.2636363636363...

2) If you have 2.2 - 1.16 with a bar above the whole expression:  this means the same thing as if you had parentheses around the expression; it means this:  (2.2 - 1.16)

To some people -- creepy -- to others -- cute -- maybe even beautiful ...

You can use the calculator in this way:  (2nd) (sin) and enter .75  --  which becomes asin(.75)

This will give you the angle, in either degrees or radians whose sin is .75.