Question

Need help with the last 2. Can't seem to find the answer choices they gave. Keep coming up with a weird fraction log answer. I'm trying to assist my child with this. How do I input this in her Ti83 calculator?

Thanks

Answer 1

Can you upload a screen shot of the actual problem?

Answer 2

I did

Answer 3

There must have been a problem with the upload since I'm not seeing any attached files

Answer 4

Trying again

Answer 5

I assume the numbers on the side is the answer that she's chosen or are they our options?

Answer 6

Yes those are the answer choices.

Answer 7

well you need to know a few log laws

\[2\log_{10}(6) ~`can~be ~written ~~\log_{10}(6^2)\]

same thing for the other term

\[\frac{1}{3} \log_{10} 27 = \log_{10} \sqrt[3]{27}\]
so if you simplify the terms you get

\[\log_{10}(36) - \log_{10}(3)\]

Answer 8

The first 3. She got the answers 4, 3 & 2

Answer 9

with logs... subtracting the terms really means you are dividing the logs

\[\log_{10}(\frac{36}{3}) = \log_{10}(x)\]

so to find x, simplify 36/3

Answer 10

is the last question also a problem... ?

Answer 11

so what you are being asked to do, is get a single log on the left side of the equation so that you can then solve for x

Answer 12

Thanks. I'll go over this with her tomorrow & see if it makes better sense to her.

Answer 13

ok as for the last question the log law you need is

\[\log_{a}(\frac{m}{n}) = \log_{a}(m) - \log_{a}(n)\]

so this means that the left side of the equation can be written as

\[\log_{7}(24) - \log_{7}(x + 5) = \log_{7}(\frac{24}{x + 5})\]

so the problem becomes

\[\log_{7}(\frac{24}{x + 5}) = \log_{7}(8)\]

since they are the same base you can then equate

\[\frac{24}{x + 5} = 8\]

which becomes

\[24 = 8(x + 5)\]

now you can solve for x

divide both sides of the equation by 8 then subtract 5.

hope it helps

Answer 14

Very much! So glad you broke it down. Makes more sense now