objective – tsw solve equations that contain “e” and natural logarithms
Post on 25-Dec-2015
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What is this “e” business about ?“e” is a number like pi.
- It is a non repeating, never ending decimal.- An irrational number.- e ≈ 2.71828…- e is the base of the natural log (ln)…just like 10 is the base of log.
Why do we use “e”Because in the natural log (ln) the base is e.
ALL PROPERTIES of logarithms apply to natural logarithms.
Anytime you see ln…you can write loge
For example: ln 3 means loge 3
Examples…Write each exponential equation in logarithmic form or each logarithmic equation in exponential form.1. ex = 8 2. e5 = x 3. e7 = x
4. ln x = 0.7741 5. ln 10 = x 6. ln x = 2.1438
Write each expression as a single logarithm.7. 3 ln 10 – ln 8 8. ln 40 + 2ln ½
+ ln x
9. 6ln 8 – 2ln 4 10. 2ln 5 + 4ln 2 + ln 5y
To Solve natural log equations:1. Identify whether the equation is in
log form or exponential form.2. Get the “log/ln” portion by itself
OR get the “exponential” portion by itself.
3. Rewrite into either log or exponential form.
4. Solve.5. Check your answer.
***REMEMBER ln means loge***
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