# Thread: Simplify the expression (log question)

1. ## Simplify the expression (log question)

Simplify
e^(x+lnx)

Without using tables or calculators determine the following
$\displaystyle log5(0.04)$ (5 is the subscript of the log)

Also, how would you express this in terms of a and b if
a = ln 2 and b = ln 3?
$\displaystyle ln 2 \sqrt 2$

Thanks!

2. Originally Posted by Skizye
Simplify
e^(x+lnx)

Without using tables or calculators determine the following
$\displaystyle log5(0.04)$ (5 is the subscript of the log)

Also, how would you express this in terms of a and b if
a = ln 2 and b = ln 3?
$\displaystyle ln 2 \sqrt 2$

Thanks!
1)
hint
use identity $\displaystyle e^{a+b} = e^a \cdot e^b \ and\ e^{\ln x}= x$
Spoiler:

$\displaystyle e^{x+ \ln x}=e^{x} \cdot e^{\ln x}=e^x \cdot x =x e^x$

2) $\displaystyle log5(0.04)$
hint:
0.04=1/25
log(a/b)=log a -log b
$\displaystyle \log_{5}{1}=0 \quad \because 5^0=1$
$\displaystyle \log_{5}{5}=1 \quad \because 5^1=5$
Spoiler:

[tex] $\displaystyle \log_{5}(0.04)=\log_{5}(\frac {1}{25})= \log_{5}{1}-\log_{5}{25}$
$\displaystyle 0-\log_{5}{(5^2)}=0-2 \log_{5}{5}=-2 \cdot 1 =-2$