# 6.7 – Base “e” and Natural Logarithms

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6.7 – Base “e” and Natural Logarithms
Objective – TSW solve equations that contain “e” and natural logarithms.

“e” is a number like pi. - It is a non repeating, never ending decimal. - An irrational number. - e ≈ … - e is the base of the natural log (ln)…just like 10 is the base of log.

On your calculators… Let’s Practice Using “e”
e e e e1/4

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

Let’s look at this “ln” business.
ln 99, ln ln ½ 4. ln (-2) 5. ln (15)

Examples…Write each exponential equation in logarithmic form or each logarithmic equation in exponential form. ex = e5 = x e7 = x 4. ln x = ln 10 = x 6. ln x =

Write each expression as a single logarithm.
3 ln 10 – ln ln ln ½ + ln x 9. 6ln 8 – 2ln ln 5 + 4ln 2 + ln 5y

To Solve natural log equations:
Identify whether the equation is in log form or exponential form. Get the “log/ln” portion by itself OR get the “exponential” portion by itself. Rewrite into either log or exponential form. Solve. Check your answer. ***REMEMBER ln means loge***

11. ex+2 = e3x + 1= 5

ln x – 1 = ln x + 2 = 6

Continuous Compound Interest

Homework… Pg. 529 #’s 1-14(all), 34, 36, 38 