# Doubt

• August 4th 2013, 09:09 PM
srirahulan
Doubt
differentiate respect to (x) $2^x$ In this case my friends do like this

$y=2^x$
$lny=xln2$
Then differentiate both side respect to x

In the second step how we take a variable in front of log,we only take a constant to the front of log.. please give me a solution
• August 4th 2013, 10:33 PM
MarkFL
Re: Doubt
The logarithmic property:

$\log_a\left(b^c \right)=c\cdot\log_a(b)$

is valid whether $c$ is a constant or variable.
• August 5th 2013, 02:08 AM
zzephod
Re: Doubt
Quote:

Originally Posted by srirahulan
differentiate respect to (x) $2^x$ In this case my friends do like this

$y=2^x$
$lny=xln2$
Then differentiate both side respect to x

In the second step how we take a variable in front of log,we only take a constant to the front of log.. please give me a solution

$y(x)=2^x=(e^{\ln(2)})^x=e^{x\ln(2)}$

.