Question

for the natural logs and log base ten, are there any rules like the "stuff rule" that are useful when evaluating or simplifying/converting?

Answer 1

cause i know that ln e is equal to 1. but what else can it be used for? besides entering into calculator. what's a great use for it? @phi

Answer 2

are you asking why we use natural log when we already have log (base 10)?
It's helpful in calculus

Answer 3

oh

Answer 4

wait, you know how you showed me the stuff rule using the base of 10? what if it wasn't the base of 10? cause one problem, i got was

5&(logbase5 8) +3^(logbase3 9)

Answer 5

5^(logbase5 8) **

Answer 6

you undo the log by making it the exponent of the log's base
in other words,
\[ 5^{\log_5 8} = 8\]

Answer 7

oh it still works like that? oh nvmd thank you

Answer 8

there is one rule which is helpful (though painful to remember)
that is the "change of base" formula
your calculator only knows base e and base 10
say you want
\[ \log_2 8 \]
you use this formula
\[ \log_2 8 = \frac{\ln 8}{\ln 2} \]
or
\[ \log_2 8 = \frac{\log 8}{\log 2} \]

or using letters
\[ \log_a x = \frac{\log_b x}{\log_b a} \]

Answer 9

oh yeah, my teacher showed me something like that :)