# Math Help - Doubt

1. ## 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

2. ## 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.

3. ## Re: Doubt

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

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