Question

Which of the following expressions is equivalent to the one shown below? (check my answer)

Answer 1

\[2\log_225 - 2\log_25 + \log_23\]

Answer 2

Answer choices:
\[\log_275\]
\[\log_243\]
\[2\log_215\]
\[2\log_223\]

Answer 3

I chose answer C.

Answer 4

@sweetburger long time no talk! do you have a minute for an old friend? :D

Answer 5

the first choice should be the right one

Answer 6

Yeahh it was :/ can you explain it please?

Answer 7

Nice name btw xD

Answer 8

\[(\frac{ 2\log(25) }{ \log(2) }) - (\frac{ 2\log(5) }{ \log(2) }) + (\frac{ \log(3) }{ \log(2) })\]

Answer 9

i didn't use a calculator but if you want to make your life easier then use one

Answer 10

oh and thx for the compliment about my username :D

Answer 11

And then what? is there a way to calculate it without a calculator?

Answer 12

Ok there is a simpler way to do this I think.

Answer 13

First write it as
\[\log_{2}(25^2)-\log_{2}(5^2)+\log_{2}(3) \] now because each term has the same base we can combine them.
\[\log_{2}(\frac{ 225 }{ 25 })+\log_{2}(3) \] this then reduces to \[\log_{2}(25 )+\log_{2}(3) \] which then can be combined to form
\[\log_{2}(75) \]

Answer 14

Typo* for the second step it should be
\[\log_{2}(\frac{ 625 }{ 25 } )+\log_{2}(3) \]

Answer 15

@Abbles sorry for not responding sooner I was afk.

Answer 16

to be honest i totally forgot about the way you did it :/

Answer 17

I mean the change of base formula is a valid way to do it except it will be hard to come to an exact answer. You would probably be stuck with a rational approximation.

Answer 18

true

Answer 19

@sweetburger thank you so much! that was extremely helpful. :)