document.write( "Question 251515: I do not know how to plug into calculator
\n" ); document.write( ". Evaluate the logarithmic equation for three values of x that are greater than -1, three values of x that are between -2 and -1, and at x = -1. Show your work. Use the resulting ordered pairs to plot the graph; submit the graph via the Dropbox. State the equation of the line asymptotic to the graph.
\n" ); document.write( "y = log4 (x + 2)\r
\n" ); document.write( "\n" ); document.write( "2. Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph; submit the graph via the Dropbox. State the equation of the line asymptotic to the graph.
\n" ); document.write( "y=3^x-4+1
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #183213 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
No calculators I know of can do base 4 logarithms so don't feel bad that you couldn't figure how to use your calculator. The base 4 logarithms can be calculated \"by hand\" if the argument, x+2, turns out to be a power of 4. So we just have to pick x's so that x+2 works out to be a power of 4.

\n" ); document.write( "What are some powers of 4 and how do we figure out an x value that makes x+2 equal to those powers of 4?
  1. Pick an integer (... -3, -2, -1, 0, 1, 2, 3, ...)
  2. Raise 4 to that power.
  3. Set that power of 4 equal to x+2.
  4. Solve for x (i.e. subtract 2 from each side).
  5. Keep track of which x goes with which integer exponent. The integer value will be the base 4 logarithm.
  6. Repeat this process until you have all the x's you need.

\n" ); document.write( "Here's some examples:
\n" ); document.write( "
\r\n" );
document.write( "n     4 to the n power     Equation to find x       x      y = log4(x+2)\r\n" );
document.write( "                                                            (same as n)\r\n" );
document.write( "0          1                  x+2 = 1               -1          0\r\n" );
document.write( "1          4                  x+2 = 4               2           1\r\n" );
document.write( "-1         1/4                x+2 = 1/4            -1.25       -1\r\n" );
document.write( "2          16                 x+2 = 16              14          2\r\n" );
document.write( "-2         1/16               x+2 = 1/6            -1.9375     -2\r\n" );
document.write( "

\n" ); document.write( "You need one more x which works out between -1 and -2. I'll leave it up to you to find it.

\n" ); document.write( "With these pairs of x and y values (the last two columns) you have ordered pairs which you can plot on a graph. The \"connect the dots\" with as smooth a curve as possible.

\n" ); document.write( "As for the asymptote, logarithmic equations have vertical asymptotes for x values that make the argument of any logarithm zero, if any. To find your asymptote set you argument to zero and solve:
\n" ); document.write( "x + 2 = 0
\n" ); document.write( "x = -2
\n" ); document.write( "So your graph will have a vertical asymptote at x = -2. \n" ); document.write( "
\n" );