1. Log Functions...Find a

Find a so that the graph of f(x) = log_a (x) contains the point (1/2, -4).

NOTE: log_a (x) = "log sub a x"

2. Originally Posted by magentarita
Find a so that the graph of f(x) = log_a (x) contains the point (1/2, -4).

NOTE: log_a (x) = "log sub a x"
(1/2,-4) will satisfy the equation
-4=log_a (1/2)
a^-4=1/2
a^4=2
therfor
a=+2^(1/4) as a can not be <0

3. Originally Posted by magentarita
Find a so that the graph of f(x) = log_a (x) contains the point (1/2, -4).

NOTE: log_a (x) = "log sub a x"
Let $\displaystyle y=\log _a x$

$\displaystyle (x, y) \implies \left(\frac12, -4\right) \implies x=\frac12, y=-4$

$\displaystyle \therefore -4 = \log _a \left(\frac12\right)$

The general rule to simplify this is: $\displaystyle \log _a n = x \implies a^x = n$

$\displaystyle \therefore -4 = \log _a \left(\frac12\right) \implies a^{-4} = \frac12$

$\displaystyle \therefore a = \sqrt[-4] {\frac12} = \left(\frac12\right)^{-\frac14}$

$\displaystyle \therefore a = (2)^{\frac14} = \sqrt[4]2 \approx 1.19\text{ to 3 s.f}$

4. Great Work!

I thank both of you, especially Air for his use of LATEX.

5. Originally Posted by magentarita
I thank both of you, especially Air for his use of LATEX.
You fell for the old gender bias trap ...... I believe that s/he is XX not XY ....