document.write( "Question 689611: How do you solve this equation? 4=ln(x+5)
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Algebra.Com's Answer #426076 by jsmallt9(3758) $\"\"$ $\"About$

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Solving equations where the variable is in the argument of a logarithm usually starts with transforming the equation into one of the following forms:
\n" ); document.write( "log(expression) = number
\n" ); document.write( "or
\n" ); document.write( "log(expression) = log(expression)

\n" ); document.write( "You equation, 4 = ln(x+5), is already in the first form. The next step with this form is to rewrite the equation in exponential form. In general $\"log%28a%2C+%28p%29%29+=+q\"$ is equivalent to $\"a%5Eq+=+p\"$ . Using this patter on your equation (and the fact the the base of ln is e):
\n" ); document.write( " $\"e%5E4+=+x+%2B+5\"$
\n" ); document.write( "Now we just subtract 5 from each side:
\n" ); document.write( " $\"e%5E4+-+5+=+x+\"$
\n" ); document.write( "This is an exact expression for the solution to your equation. If you want/need a decimal approximation then just use your calculator to evaluate the left side. (If your calculator does not have a button for the number \"e\", then use 2.7182818284590452353602874713527 (or some rounded off version of this).)
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