7.4 Notes

Logarithm: the inverse of an exponential function. It describes the exponent needed to produce a given answer.
y  log a x
(a ≠ 1, a > 0, x > 0 ).
For example, the logarithmic form is y = log5 125 where the exponent = y, the yielded number = 125 and the base
= 5. The exponential form is 5y = 125 and the y value is 3
logarithmic form: y = log5 125
exponential form: 5y = 12 in both cases y = 3
The red line shows the exponential function.
The green line is the line of reflection.
The blue line shows the logarithmic function.
Common Logarithm: Logarithms to the base 10.
Calculators evaluate logs to the base 10.
Natural Logarithm: the logarithm base e of a number. The natural logarithm of x is written ln x. For example, ln 8
is 2.0794415... since e2.0794415... = 8. They are called natural because they occur in biology and the social sciences in
natural situations that involve growth or decay