Question

Can someone please explain how you would solve "log(7)343 as a logarithm with base 7"

Answer 1

See:

\[\large{\log_{a} a^b = b}\]

Answer 2

Now, if you notice that:

\[\large{343 = 7^3}\]

Answer 3

So, the problem you are asking for becomes:

\[\large{\log_{7} 7^3}\]

compare this with the formula:

\(\color{blue}{\text{Originally Posted by}}\) @vishweshshrimali5
\[\large{\log_{a} a^b = b}\]
\(\color{blue}{\text{End of Quote}}\)

What do you think the answer must be ?

Answer 4

there is also a nice method to cheat, if you do not know that \(7^3=343\)

Answer 5

Use a calculator ?

Answer 6

:D

Answer 7

whip out mr calculator and type in
\[\log(343)\div \log(7)\]

Answer 8

Hahaha :D

Best method @satellite73 and probably the most used ^^^

Answer 9

Oh..Now I get it. Thanks guys. I just didn't understand what numbers you would plug into the calculator

Answer 10

Great :)

Answer 11

actually i was being silly
it will work of course but this was not really a calculator exercise

Answer 12

So what about if I had \[\log _{49}343\] with a base of 7

Answer 13

if you want the calculator method, replace the \(7\) by \(49\)
there is another method, but it requires some thinking

Answer 14

I just need to know the calculator method for now but thank you. So you basically just ignore the "with a base of 7" part and use 49?

Answer 15

Actually what satellite is doing is the process called conversion of base.

Answer 16

Yah isn't it the \[\log _{b}y\]=\[\frac{ \log _{y} }{ \log }\]

Answer 17

Well afraid not

Answer 18

It is basically this:

\[\large{\log_a b = \cfrac{\log_c b}{\log_c a}}\]

Answer 19

Oh. Thank you so much!