document.write( "Question 615808: 2e^x -5=1 \n" ); document.write( "

Algebra.Com's Answer #387310 by Theo(13342) $\"\"$ $\"About$

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2e^(x-5) = 1
\n" ); document.write( "divide both sides of the equation by 2 to get:
\n" ); document.write( "e^(x-5) = 1/2
\n" ); document.write( "take the natural log of both sides of the equation to get:
\n" ); document.write( "ln(e^(x-5) = ln(1/2)
\n" ); document.write( "since log(a^b) = b*log(a), this equation becomes:
\n" ); document.write( "(x-5)*ln(e) = ln(1/2)
\n" ); document.write( "divide both sides of this equation by ln(e) to get:
\n" ); document.write( "x-5 = ln(1/2)/ln(e)
\n" ); document.write( "since ln(e) = 1, this equation becomes:
\n" ); document.write( "x-5 = ln(1/2)
\n" ); document.write( "add 5 to both sides of this equation to get:
\n" ); document.write( "x = ln(1/2) + 5
\n" ); document.write( "use the LN function of your calculator to solve for x to get:
\n" ); document.write( "x = 4.306852819
\n" ); document.write( "replace x with 4.306852819 in your original equation and you'll find that the equation is true (1 = 1)
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