Question

see attachment.

Answer 1

Maybe this will help a little... here's how you can expand a log statement with a fraction like this problem:
\[\log _{b}\frac{ m }{ n } = \log _{b}m - \log _{b}n\]

Answer 2

i don't understand. what does log mean anyhow

Answer 3

@surdawi

Answer 4

I'm not sure I am good at explaining it... @surdawi, feel free to help :)

Logarithms are sort of like the opposite of exponents. So log rules can help you solve problems where you have unknowns in your exponents.

Answer 5

so i have to find out what exponent equals to 729

Answer 6

do what @JakeV8 said

\[\log_{3} \frac{ 1 }{ 729 }=\log_{3}1-\log_{3}729\]
log 1 = 0
\[\log_{3}729=\frac{\log_{10} 729}{\log_{10} 3}\]
plug in to the calculator what do you get for log729?

Answer 7

i dont know how to plug it in the caculato

Answer 8

She isn't supposed to use the calculator... is there a way to simplify without the calculator?

Answer 9

3^x=729?

Answer 10

i have to go for now bbl tonight

Answer 11

Yes, that's what I would say too...

View it like: log_3 ( 729) means "3 raised to some power is 729"
What is that power?

Answer 12

3^2 = 9
3^3 = 27
etc

Answer 13

ok thanks guys

Answer 14

Good luck!

Answer 15

Thank you @JakeV8

Answer 16

so i got 3^6=729 Now what!

Answer 17

is the answer is y=6

Answer 18

that's just the 2nd half of that equation from earlier... you also had log_3 of 1, which is 0.

So it was log_3 (1) - log_3(729) = 0 - 6 = -6

Answer 19

is that a negative 3

Answer 20

no, that's the "log base 3" from your problem.\[\log _{3}\frac{ 1 }{ 729 }= \log _{3}1 - \log _{3}729 = 0 - 6 = -6\]

Answer 21

ok thank you

Answer 22

glad to help :)