Inverse functions
The three log laws
Evaluate $\log_6 4 + \log_6 9$ and $\log_2 48 - \log_2 3$.
$\log_6 (4 \times 9) = \log_6 36 = 2$
$\log_2 \dfrac{48}{3} = \log_2 16 = 4$
Given $\log_a 2 = p$ and $\log_a 3 = q$, write $\log_a 12$ and $\log_a \tfrac{9}{2}$ in terms of $p$ and $q$.
$\log_a 12 = \log_a (2^2 \times 3) = 2p + q$
$\log_a \tfrac92 = \log_a 3^2 - \log_a 2 = 2q - p$
Simplify $2\log_{10} 5 + \log_{10} 4$.
$\log_{10} 25 + \log_{10} 4 = \log_{10} 100 = 2$
Power law first, then the product law.
$log_a xy$
$\log_a x + \log_a y$
$log_a rac{x}{y}$
$\log_a x - \log_a y$
Evaluate $\log_6 4 + \log_6 9$.
Evaluate $\log_2 48 - \log_2 3$.
Evaluate $\log_2 8^5$.
$5\log_2 8 = 5 \times 3 = 15$.
$\log_a \dfrac1x$ equals:
$\log_a 1 - \log_a x = -\log_a x$.
If $\log_a 2 = p$ and $\log_a 3 = q$, then $\log_a 12$ is:
Evaluate $5^{\log_5 7}$.
The power and the log undo each other.
$\dfrac{\log_a 8}{\log_a 2}$ equals:
$\dfrac{3\log_a 2}{\log_a 2} = 3$.
Which statement is false?
There is no law for the log of a sum.
Evaluate $\log_{10} 25 + \log_{10} 4$.
New numbers every time. Keep going until you get five in a row.
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