anonymous
  • anonymous
Evaluate log base 3(400) to five decimal places
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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phi
  • phi
Evaluate log base 3(400) to five decimal places First, this problem requires a calculator or computer to solve. The trouble is that most (all?) calculators do not do log base 3. They do know log base 10 (labeled log) and log base e (labeled ln). We will use ln (natural log) To solve this problem, it is very important to know that \[ log_3(400)=x \] is the same problem as \[ 400 = 3^{x} \] If this seems strange, you might want to watch http://www.khanacademy.org/math/algebra/logarithms/v/introduction-to-logarithms Take the ln of both sides \[ ln(400)= ln(3^{x}) \] Now use the exponent rule of logs (See http://www.khanacademy.org/math/algebra/logarithms/v/logarithm-of-a-power ) \[ ln(400) = xln(3) \] Divide both sides by ln(3): \[ \frac{ln(400)}{ln(3)}=x \] If you cut and paste ln(400)/ln(3)= into the google window it will calculate the answer: 5.45366606 Finally, round the answer to 5 decimal places. Count to the 6th decimal place 123456 5.453666 It is 6, (5 or bigger) so make the 5th decimal one bigger: 5.45367 That is the answer.

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