Download Properties of Logarithms (Sec

Properties of Logarithms (Sec. 12.5)
Product Property of Logarithms
If x, y, and b are positive real numbers and b ≠ 1, then logb xy  logb x  logb y .
WHY?
Write each sum as a single logarithm.
a. log11 10  log11 3
c. log2  x  2  log2 x
b. log5 3  log 4 3
Quotient Property of Logarithms
If x, y, and b are positive real numbers and b ≠ 1, then logb
x
 logb x  logb y .
y
Write each difference as a single logarithm.
a. log10 27  log10 3
b. log5 8  log5 x
c. log 5  x 2  5   log 5  x 2  1
Power Property of Logarithms
If x, y, and b are positive real numbers, b ≠ 1, and r is a real number, then log b x r  r log b x .
Use the power property to rewrite each expression.
a. log 5 x 3
b. log 4 2
c. log b 2 x
OYO: log5 3  log5  x  2
OYO: log 2 14  log 2 7
OYO: log 3 5 x
Write the following as a single logarithm.
a. 2log5 3  3log5 2
b. 3log9 x  log9  x  1
c. log 4 25  log 4 3  log 4 5
Write each expression as sums or differences of multiples of logarithms.
a. log 3
57
4
b. log 2
x5
y2
c. log
x3
2
OYO: Write as a single logarithm
OYO: Write as sums or differences of logarithms
3log3 4  4log3 2
log 7
x3 y
2