document.write( "Question 88611This question is from textbook
\n" ); document.write( ": How do you find a solution of the exponential equation, correct to four decimals places.
\n" ); document.write( "20. 10^1-x = 6^x \n" ); document.write( "

Algebra.Com's Answer #64417 by Earlsdon(6294) $\"\"$ $\"About$

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You can use logarithms to solve exponential equations.
\n" ); document.write( " $\"10%5E%281-x%29+=+6%5Ex\"$ Take the commom logarthim of both sides.
\n" ); document.write( " $\"Log%5B10%5D%2810%5E%28%281-x%29%29%29+=+Log%5B10%5D%286%5Ex%29\"$ Apply the power rule for logarithms.
\n" ); document.write( " $\"%281-x%29Log%5B10%5D%2810%29+=+x%2ALog%5B10%5D%286%29\"$ Recall that $\"Log%5B10%5D%2810%29+=+1\"$
\n" ); document.write( " $\"%281-x%29+=+x%2ALog%5B10%5D%286%29\"$ Add x to both sides.
\n" ); document.write( " $\"1+=+x%2BxLog%5B10%5D%286%29\"$ Factor out the x.
\n" ); document.write( " $\"1+=+x%281%2BLog%5B10%5D%286%29%29\"$ Divide both sides by $\"1%2BLog%5B10%5D%286%29\"$
\n" ); document.write( " $\"1%2F%281%2BLog%5B10%5D%286%29%29+=+x\"$ Evaluate this.
\n" ); document.write( " $\"1%2F%281%2B0.778%29+=+x\"$
\n" ); document.write( " $\"x+=+1%2F1.778\"$
\n" ); document.write( " $\"x+=+0.56243\"$ \n" ); document.write( "

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