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logarithm of a product
01 - Solution of Logarithmic Equations
Solve for x from the following:
$\log_6 (x - 2) + \log_6 (x + 3) = 1$
$x^{\log x} = 10\,000$
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Logarithm and Other Important Properties in Algebra
Properties of Logarithm
If $y = a^x$, then $\log_a y = x$. ← Definition of logarithm
$\log_a xy = \log_a x + \log_a y$
$\log_a \dfrac{x}{y} = \log_a x - \log_a y$
$\log_a x^n = n \log_a x$
$\log_a a = 1$
$\log_a 1 = 0$
$\log_{10} x = \log x$ ← Common logarithm
$\log_e x = \ln x$ ← Naperian or natural logarithm
$\log_y x = \dfrac{\log x}{\log y} = \dfrac{\ln x}{\ln y}$ ← Change base rule
If $\log_a x = \log_a y$, then $x = y$.
If $\log_a x = y$, then $x = {\rm antilog}_a \, y$.
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15 - Sum of Circumference af all the Circles
Files for Download are Now Available to Non-logged-in Users
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Problem 5: Evaluate $\displaystyle \int \dfrac{(6z - 1) \, dz}{\sqrt{(2z + 1)^3}}$ by Algebraic Substitution
Problem 4: Evaluate $\displaystyle \int \dfrac{y \, dy}{\sqrt[4]{1 + 2y}}$ by Algebraic Substitution
Problem 3: Evaluate $\displaystyle \int \dfrac{x^3 \, dx}{(x^2 + 1)^3}$ by Algebraic Substitution
Problem 2: Evaluate $\displaystyle \int y^3\sqrt{2y^2 + 1} \,\, dy$ by Algebraic Substitution
Which curve has a constant first derivative?
Exam: Bonus Set (HydroGeo)
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