Hi! Can anyone explain to me how to calculate log(x) without a calculator? For example log81 and log36 ?? I just learned logarithms and familiar with how it is written using bases but there is nothing that explains this to me. Also how does 3^x = 81 become xlog3 = log81 ??

Question

Hi! Can anyone explain to me how to calculate log(x)     without a calculator?   For example  log81    and log36   ??   I just learned logarithms and familiar with how it is written using bases but there is nothing that explains  this to me.    Also how does   3^x = 81   become    xlog3 = log81   ??

anonymous · Answer

hmm ok i just found that  the base is 10 for  log(x)

mathstudent55 · Answer

To answer your second question first, here's a rule of logs:

$ \log x^n = n \log x$

Also, if you have an equation, you can take the log of both sides.

Start with 
$3^x = 81$

First, take the log of each side:

$ \log 3^x = \log 81$

Use the rule above:

$x \log 3 = \log 81$

We can go further, if you realize that $ 81 = 3^4$

$ x \log 3 = \log 3^4$

$x \log 3 = 4 \log 3$

$x = \dfrac{4 \log 3}{\log 3} $

$x = 4$

anonymous · Answer

ok thanks for some reason that rule is not shown in my module, also does not state that log(x) uses a common base of 10.... -.-   thanks!!