Lab 6 Preparation
1. Reviewing the algebraic properties of logarithms.
If b > 0, b ? 1, a > 0, c > 0 and r is any real number, then:
$\log_b(ac) = \log_b a + \log_b c$ (Product property)
$\log_b(\frac{a}{c}) = \log_b a - \log_b c$ (Quotient property)
$\log_b(a^r) = r \log_b a$ (Power property)
(a) Solve the equation.
$\log_7(5x + 1) = \log_7 10 + \log_7 12$
(b) Solve the equation.
$\ln(10x) = \ln 18 - \ln 6$
(c) Use algebraic properties of logarithms to show that
$\log(\frac{x^2}{y^3}) + 5 \log y - 6 \log \sqrt{xy} = \log(\frac{1}{xy})$