7-6 Natural Logarithms
Natural base exponential function: y=ex
Natural base e : is the irrational number it is approaching
Natural log: logex or ln x
Natural log function: y=ln x (is the inverse of the natural base y=ex)
Evaluate natural logs:
ln
(ex) ln 1.2
1.2
0.1823
Plug into your calculator!
Write each expression as a single natural logarithm:
(ex)
(ex)
–
Solve each equation:
(ex)
ln 3x = 6
Loge 3x = 6
e6 = 3x
(28) ln (t-1)2=3
Loge (t-1)2 = 3
e3 = (t-1)2
+1
+1
Use natural logarithms to solve each equation:
(34) e2x =10
loge 10 = 2x
ln 10=2x
(ex)
ex+1 =30
loge 30 = x+1
ln 30 = x+1
(ex)
e3x +5=6
e3x =1
loge 1 = 3x
ln 1 = 3x