LOGARITHMSThe inverse of the exponential function-- The Natural LogarithmThe graph of y = ex clearly shows that it is a one to lớn one function, hence an inverseexists. We điện thoại tư vấn this inverse the naturallogarithm. And write it as y = ln x Below is the graph of y = ex andy = ln xBy definition, they are reflections of each other across theline y = x.
 Inverse Properties of LogsSince logs & exponents cancel each other we have:eln x = xandln ex = xExampleeln 3 =3andln(e5) = 5 Three Properties of Logs Property 1: ln (uv) = ln u + ln v (The product to Sum Rule) Property 2: ln (u/v) = ln u - ln v (The Quotient to lớn Difference Rule) Property 3: ln ur = r ln u (The power nguồn Rule) Example:Expand: ln (xy2/z)by property 2 we have:ln (xy2) - ln zby property 1 we haveln x + ln y2 - ln zBy property 3 we haveln x + 2 ln y- ln zExerciseTry to expand  The key lớn solving equations is khổng lồ know how khổng lồ apply the inverseof a function. When we have an exponential equation, we will use thenatural logarithm khổng lồ cancel the exponential. Example Find k if 34 = e10k Solution Take the natural logarithm of both sides ln 34 = ln e10k Now use the inverse property ln 34 = 10k Finally divide by 10 ln 34= k = 0.3526 10 Carbon Dating All living beings have a certain amount of radioactive carbon C14 in their bodies. When the being dies the C14 slowly decays with a half life of about 5600 years. Suppose a skeleton is found in Tahoe that has 42% of the original C14. |
The 11 Natural Log Rules You Need To Know
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