Section 11.4: Logarithms (Day 1)
May 05, 2015
11-4: Logarithmic Functions
Logarithm - A quantity representing the power/exponent
to which a fixed number (the base) must be raised to produce
a given number
In the function x = ay, y is the logarithm of x.
Logarithmic Function:
x = ay
y = loga x
Read as, "y equals the
log, base a, of x"
Write each equation in logarithmic form.
1.) 43 = 64
2.) 3-3 = 1
27
3.) 210 = 1024
Pre­Calculus
4.) 160 = 1
Section 11.4: Logarithms (Day 1)
May 05, 2015
Write each equation in exponential form.
1.) log125 25 = 2
3
2.) log82 = 1
3
3.) log27 3 = 1
3
4.) log16 4 = 1
2
Common Logarithms - logarithm with base 10
Change of Base Formula.
loga n = logbn
logba
The "log" button on your TI-83/84 graphing calculator is
programmed to be log base 10. Thus to actually be able to
enter a logarithm with a different base, we must use the
change of base formula.
*Helpful Hint: Check have logBASE on your calculator (Math Key under Math Tab)
If this is programmed on your calculator, won't need to use the change of base formula*
Pre­Calculus
Section 11.4: Logarithms (Day 1)
May 05, 2015
Evaluate each expression.
2.)
1.) log9 81
3.)
log5
1
625
log7
4.) log4 128
Solve each equation.
1.) 2x = 1/8
2.) 106x = 1
3.) log2 (3x + 1) = 5
4.) log 3x = 1
*Everything we did today can be
checked by using your calculator*
Pre­Calculus
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