1. ## logs

How do I solve the following without using my calculator:

a) e^In 1000
b) log10(100e)
c) In e
d) log10 (e^8)

2. Originally Posted by princess_anna57
How do I solve the following without using my calculator:

a) e^In 1000
b) log10(100e)
c) In e
d) log10 (e^8)
hints:

for $\displaystyle a>0, b>0, d>0$ and any $\displaystyle c \in \mathbb{R}$
$\displaystyle e^{\ln a}=a$
$\displaystyle \log_a a = 1$
$\displaystyle log_a b^c = c \log_a b$
$\displaystyle \log_a (bd) = \log_a b + \log_a d$
$\displaystyle \log_a \left(\frac{b}{d}\right) = \log_a b - \log_a d$

3. ## :)

So for a) the answer is 1,000?

4. Originally Posted by princess_anna57
So for a) the answer is 1,000?
right!

5. ## =)

and d) is 8 log 10e?

I still don't know how to do b) or c).

6. Originally Posted by princess_anna57
and d) is 8 log 10e?

I still don't know how to do b) or c).
assuming you meant $\displaystyle 8 \log_{10} e$, then you are right..

for b) $\displaystyle \log_{10} (100e) = \log_{10} 100 + \log_{10} e = \log_{10} 10^2 + \log_{10} e = ...$

for c) take note that $\displaystyle \ln a = \log_e a$.. $\displaystyle (a>0)$