document.write( "Question 714766: i want the answer of this question with steps and without logarithm formula
\n" ); document.write( "5=10^x
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #438978 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
What does \"without logarithm formula\" mean? If it means ...
  • without using logarithms, then it will be impossible to express the exact answer without logarithms. This is so because no one knows what power of 10 results in a 5. The best one could do is...
    • use a graphing technique to find an approximate value for x:
      1. Subtract 5 from each side which gives us:
        \n" ); document.write( "\"0+=+10%5Ex-5\"
      2. Use a graphing calculator to graph the related equation:
        \n" ); document.write( "\"y+=+10%5Ex-5\"
      3. Use the trace function on your calculator to find the x-coordinate of the point where the graph crosses the x-axis (where the y-coordinate is zero).
    • Use techniques learned in Calculus
  • express the answer without logarithms, then...
    1. Fing the base 10 log , \"log\", of each side:
      \n" ); document.write( "\"log%28%285%29%29+=+log%28%2810%5Ex%29%29\"
    2. Use a property of logarithms, \"log%28a%2C+%28p%5En%29%29+=+n%2Alog%28a%2C+%28p%29%29\", to move the exponent on the 10 out in front of the log:
      \n" ); document.write( "\"log%28%285%29%29+=+x%2Alog%28%2810%29%29\"
      \n" ); document.write( "Since log(10) = 1 this simplifies to:
      \n" ); document.write( "\"log%28%285%29%29+=+x\"
      \n" ); document.write( "This is an exact expression for the solution. To express this without logarithms, we can use our calculators to find a decimal approximation for log(5), making x approximately equal to: 0.69897000433601880478626110527551
  • Other???
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