## Audrae_World 3 years ago Use properties of logarithms to expand the loarithmic expressions as much as possile. log_4 7-2 1) 7log4 4 2) 4log4 7 3) -4log4 7 4) -16log 7

1. saifoo.khan

7-2?

2. Audrae_World

7-^2

3. saifoo.khan

$\log_4 7^{-2} \to \log_4 (\frac{1}{49})\to \frac{\log \frac{1}{49}}{\log 4}$

4. saifoo.khan

are the options you wrote correct? @Audrae_World

5. Audrae_World

Yes, that's what my book says

6. Calcmathlete

Isn't it $\log_{4} 1 - \log_{4} 7^{2}$

Its expand not solve @saifoo.khan

8. saifoo.khan

Yes! im stuck. :/

@Audrae_World : Is it $\log_{4} 7^2$

10. Audrae_World

That's the closest I've seen so far, but the one of answer choices says: 4log_4 7^2

11. Calcmathlete

Are you sure the problem is $\log_{4} 7^{-2}$ ?

12. Audrae_World

Yes

13. Calcmathlete

Oh. I got it. Hold on.

14. Calcmathlete

$\log_{4}7^{-2} = -2(\log_{4}7) = -2(\log_{7}7/\log_{7}4) = -2(1/\log_{7}2^{2})$ $-2(\log_{7}2^{-2}) = -2 * -2(\log_{7}2) = 4\log_{7}2$

15. Calcmathlete

Wait. Darn it...

LOL @Calcmathlete :whats that !??

17. Calcmathlete

lol. I got so close!!! But then I realized that it isn't one of the answers...