document.write( "Question 202690: I am having trouble with finding the domain for expressions like f(t)=log(t-5), g(x)=5e^x, g(x)=ln(x+4) and g(t)= 5^t. The concept eludes me, can anyone help with how to go about solving these??\r
\n" ); document.write( "\n" ); document.write( "E.T. \n" ); document.write( "
Algebra.Com's Answer #152883 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
the domain is the possible values that x can take.
\n" ); document.write( "the range is the possible values that y can take.
\n" ); document.write( "domain is possible values that x can take.
\n" ); document.write( "range is the possible values that y can take.
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\n" ); document.write( "your first problem:
\n" ); document.write( "f(t) = log(t-5)
\n" ); document.write( "you cannot take the log of any number that is 0 or less than 0.
\n" ); document.write( "your equation is y = log(t-5)
\n" ); document.write( "your domain is (t-5)
\n" ); document.write( "your range is log(t-5)
\n" ); document.write( "in this case (t-5) must be greater than zero which means that t must be > 5.
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\n" ); document.write( "your second problem is g(x) = ln(x+4).
\n" ); document.write( "same deal.
\n" ); document.write( "you cannot take the natural log of any number if it is 0 or less.
\n" ); document.write( "your equation is y = ln(x+4)
\n" ); document.write( "your domain is x+4 and your range is y which is ln(x+4)
\n" ); document.write( "your domain has to be > 0, so x+4 have to be > 0 which can only be if x > -4.
\n" ); document.write( "your domain is x > -4
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\n" ); document.write( "your third problem is g(x) = 5e^x
\n" ); document.write( "this is the same as y = 5e^x
\n" ); document.write( "x is your domain.
\n" ); document.write( "5e^x is your range.
\n" ); document.write( "in this particular case, there does not appear to be any restrictions to the value of x.
\n" ); document.write( "x can be any real number (negative, 0, or positive).
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\n" ); document.write( "your fourth problem is g(t) = 5^t.
\n" ); document.write( "this is the same as y = 5^t.
\n" ); document.write( "there do not appear to be any restrictions to the value of t, which is your domain.
\n" ); document.write( "t is your domain.
\n" ); document.write( "5^t is your range.
\n" ); document.write( "t can be any real number (negative, 0, or positive).
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\n" ); document.write( "exponents and logs are inverse relationships to each other.
\n" ); document.write( "if it wasn't for exponents, logarithms would not exist.
\n" ); document.write( "the rules are:
\n" ); document.write( "y = b^x if and only if x = \"log%28b%2Cy%29\"
\n" ); document.write( "if y = b^x, the inverse function is y = \"log%28b%2Cx%29\"
\n" ); document.write( "while x in the exponent equation can be any real number, x in the logarithm equation has to be > 0.
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\n" ); document.write( "in any equation, if y = f(x), x is the domain, and f(x) is the range.
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\n" ); document.write( "I hope this answers your quesation.
\n" ); document.write( "If it doesn't, send me an email with the specific area of discomfort, and I'll try to ease it for you.
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