document.write( "Question 384987: 7+3In x=6 \n" ); document.write( "

Algebra.Com's Answer #272787 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
7 + 3ln(x) = 6
\n" ); document.write( "First let's isolate the logarithm. Subtracting 7 from each side we get:
\n" ); document.write( "3ln(x) = -1
\n" ); document.write( "Divide both sides by 3:
\n" ); document.write( " $\"ln%28x%29+=+-1%2F3\"$
\n" ); document.write( "Once we have isolated (or \"solved for\") the logarithm, the next step is to rewrite the equation in exponential form. In general $\"log%28a%2C+%28p%29%29+=+q\"$ is equivalent to $\"p+=+a%5Eq\"$ . Using this pattern on your equation (and remembering that the base of the ln logarithm is e) we get:
\n" ); document.write( " $\"x+=+e%5E%28-1%2F3%29\"$
\n" ); document.write( "This is an exact expression for the solution to your equation. If you need a decimal approximation then you can use your calculator on the exact expression. (If your calculator has a button for the number e and if it has buttons for parentheses you can just type in:
\n" ); document.write( "e^(-1/3)
\n" ); document.write( "If your calculator has no buttons for parentheses, use
\n" ); document.write( "e^-0.33333333
\n" ); document.write( "If your calculator has no buitton for e, use
\n" ); document.write( "2.7182818284590452353602874713527^-0.33333333
\n" ); document.write( "(Round off these decimals as you see fit.) \n" ); document.write( "

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