1. ## Logarithms Properties/Identities/Etc.

Need some help on these, just to make sure I understand what I'm doing...

1) If $\displaystyle \log_ba = x$ then $\displaystyle \log_ab =$

$\displaystyle \frac{1}{\log_ab}$

2) If $\displaystyle \log_ba = x$ then $\displaystyle \log_\frac{1}{b}a =$

$\displaystyle -\log_ba$

3) $\displaystyle \log(2 - x) + \log(3 - x) = \log12$ solve for x

$\displaystyle x = -1$

4) $\displaystyle y = \log_bx + \log_b(x - 6)$ solve for x

$\displaystyle b^y = x^2 - 6x$

then...

would the quadratic formula be used?

$\displaystyle x^2 - 6x - b^y = 0$

??

2. Originally Posted by JSB1917
4) $\displaystyle y = \log_bx + \log_b(x - 6)$ solve for x

$\displaystyle b^y = x^2 - 6x$

then...

would the quadratic formula be used?

$\displaystyle x^2 - 6x - b^y = 0$

??
To solve for x yes, use $\displaystyle a=1, b=-6$ and $\displaystyle c = - b^y$

3. Originally Posted by pickslides
To solve for x yes, use $\displaystyle a=1, b=-6$ and $\displaystyle c = - b^y$
Ok, so it would come out to...

$\displaystyle x = \frac {6 \pm \sqrt{36 + 4b^y}}{2}$

$\displaystyle x > 6$

4. Originally Posted by JSB1917
Need some help on these, just to make sure I understand what I'm doing...

1) If $\displaystyle \log_ba = x$ then $\displaystyle \log_ab =$

$\displaystyle \frac{1}{\log_ab}$

2) If $\displaystyle \log_ba = x$ then $\displaystyle \log_\frac{1}{b}a =$

$\displaystyle -\log_ba$
Ok, I'm confused. My teacher marked both of these wrong. Instead he wanted $\displaystyle \frac {1}{x}$ for the first and -x for the second, but isn't what I put essentially the logical equivalence of the answers?

I got a zero for both of these. I had to turn back in the HW sheet because he completely missed a problem and gave a zero for it and I didn't have time to think about these two at the moment.

I can't understand why I shouldn't get at least 1 point for both of the problems, even though he wanted the work shown.

5. Originally Posted by JSB1917
Need some help on these, just to make sure I understand what I'm doing...

1) If $\displaystyle \log_ba = x$ then $\displaystyle \log_ab =$

2) If $\displaystyle \log_ba = x$ then $\displaystyle \log_\frac{1}{b}a =$

3) $\displaystyle \log(2 - x) + \log(3 - x) = \log12$ solve for x

(1) $\displaystyle \frac{1}{\log_ab}=x \Rightarrow \log_ab=\frac{1}{x}$

(2) $\displaystyle \frac{1}{log_a\frac{1}{b}}=\frac{1}{-log_ab}=-\frac{1}{x}$

(3)log (2-x)(3-x)=log 12

x^2-5x-6=0

(x-6)(x+1)=0

Continue solving here .

..
wait what?

Also I noticed a typo earlier, it's supposed to be for number one.

$\displaystyle \frac {1}{\log_b a}$

7. Originally Posted by JSB1917
wait what?

Also I noticed a typo earlier, it's supposed to be for number one.

$\displaystyle \frac {1}{\log_b a}$
edited , so clear now ?