document.write( "Question 201505: Question: find the domain, vertical asymptote, and the x-intercept of f(x)=log(subscript 4)(5-x). \n" ); document.write( "
Algebra.Com's Answer #151745 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
Domain: The arguments to any logarithm function, no matter what the base, must always be positive. So to find the domain we just have to solve:
\n" ); document.write( "\"%285-x%29+%3E+0\"
\n" ); document.write( "Adding x to both sides gives us
\n" ); document.write( "\"+5+%3E+x+\" which says x is less than 5. (Always read inequalities from where the variable is! In this case we read it from right to left, since x is on the right, which is why it is a less than.)
\n" ); document.write( "The domain is all numbers less than 5.
\r
\n" ); document.write( "\n" ); document.write( "Vertical asymptote: For logarithm functions the vertical asymptote will be for x values that would make the argument zero. So we solve
\n" ); document.write( "\"5+-+x+=+0\"
\n" ); document.write( "Again adding x to both sides we get
\n" ); document.write( "\"5+=+x\"
\n" ); document.write( "So the vertical asymptote is the line: x = 5
\r
\n" ); document.write( "\n" ); document.write( "The x-intercepts of a function is where the y-value is 0. So we need to solve
\n" ); document.write( "0 = log(base4)(5-x)
\n" ); document.write( "If we understand exponents and logarithms, this is easy. This equation says that 0 (zero) is the exponent you put on 4 to get (5-x). But a zero exponent on any number (except 0) always results on 1! So this equation means that (5-x) must be 1.
\n" ); document.write( "Solving
\n" ); document.write( "\"5-x+=+1\"
\n" ); document.write( "Subtract 5 from both sides giving
\n" ); document.write( "\"-x+=+-4\"
\n" ); document.write( "Dividing (or multiplying) both sides by -1 we get
\n" ); document.write( "\"+x+=+4+\"
\n" ); document.write( "So our only x-intercept is (4, 0).
\n" ); document.write( " \n" ); document.write( "
\n" );