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Mastering Natural Logarithms: Easy Step-by-Step Guide

Learn to solve equations involving natural logarithms with this comprehensive guide. Understand ln equations, exponentially rewrite expressions, and apply log properties. Practice with examples and step-by-step solutions provided. Excel in logarithmic functions effortlessly!

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Mastering Natural Logarithms: Easy Step-by-Step Guide

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  1. Warm-Up 5/6 1. Find the value of 2.3869 50,625 2. Solve.

  2. 11.6 Natural Logarithms • Natural logarithms are just like the logarithms we’ve been using in previous sections. • The only difference is they are in base “e”. • Whenever we have an equation with “e” we will use the natural logarithm • They are written: • ln x = logex • What is ln e = ? • e ^ ? = e ………..1st power • Therefore: ln e = 1 • What is ln 1 = ? Think about it……… 0 “log base b to number 1 is always 0 just for fun”

  3. Easy stuff: type into calculator • ex1: evaluate ln0.0089 • -4.7217 • Ex2: evaluate antiln(-0.7831) • 0.4570 • You probably won’t see “antiln” too often, it makes more sense to write it how?? • ex

  4. Ex3: solve: 7.2=-28.8 lnx • Divide by -28.8 • Re-write in exponential form • Plug into calc and solve

  5. Ex: 12ex= 108 • Always try to get the “exponential term” alone first (divide by 12) • Now take the ln of both sides • solve ex = 9 lnex = ln9 xlne = ln9 x=2.20

  6. Ex4: solve using natural logs52x = 7x+1 • Take the natural log of both sides • Use your log properties “finding answers in the hunt powers of logs can go up front” • Divide by the natural log 1st, either side, you pick • Solve the problem, no logs anymore

  7. Ex 5: solve 4.5 > e0.031t • Take natural log of both sides • Use properties • Remember lne = 1 • Solve away  divide by .031 1 t < 48.5186

  8. Assignment • 11.6 p. 736 #19 – 35 odds, 36 – 43 all

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