Question

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 $\log(\frac{x^2}{y^3}) + 5 \log y - 6 \log \sqrt{xy} = \log(\frac{1}{xy})$

          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
$\log(\frac{x^2}{y^3}) + 5 \log y - 6 \log \sqrt{xy} = \log(\frac{1}{xy})$

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:
(ac) = a + c (Product property)
((a)/(c)) = a - c (Quotient property)
(a^r) = r a (Power property)
(a) Solve the equation.
log7(5x + 1) = log7 10 + log7 12
(b) Solve the equation.
ln(10x) = ln 18 - ln 6
(c) Use algebraic properties of logarithms to show that
log((x^2)/(y^3)) + 5 log y - 6 log√(xy) = log((1)/(xy))

Added by Mar H.

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