Hi there,
I have a question, how do you evaluate the following without a calculator?
log2(log3(log5^125)))
Thanks
ps. log2, log3 and log5 are the bases
Err doesn't really make sense.
Do you mean:
$\displaystyle \log_2(\log_3(\log_5(125))) $?
If so, take the very first term, and set it equal to y:
$\displaystyle y = \log_5(125) $
This means that $\displaystyle 5^y = 125 $
You should be able to tell that $\displaystyle 125 = 5^3 $, and hence $\displaystyle y = 3 $.
So now you have:
$\displaystyle \log_2(\log_3(3)) $
Now take that term again, and set it equal to another variable, x.
$\displaystyle x = \log_3(3) $
$\displaystyle 3^x = 3 $. Clearly $\displaystyle x = 1$
This gives:
$\displaystyle \log_2(1) $
Set it equal to a random variable:
$\displaystyle z = \log_2(1) $
$\displaystyle 2^z = 1 $
Clearly $\displaystyle z = 0 $