Notes: How to find x if 11^(2x+1)=13.

Thursday, August 15, 2013

The equation 11^(2x+1)=13 has to be solved for
x.

11^(2x+1)=13

Take the
logarithm of both the sides

$\displaystyle{\log{{\left({{11}}^{{{2}{x}+{1}}}\right)}}}={\log{}}$
13

Use the property of logarithm $\displaystyle{{\log{{a}}}}^{{b}}={b}\cdot{\log{}}$
a

$\displaystyle{\left({2}{x}+{1}\right)}\cdot{\log{{11}}}={\log{}}$
13

Isolate x to one of the
sides

$\displaystyle{2}{x}+{1}=\frac{{{\log{{13}}}}}{{{\log{}}}}$
11)

$\displaystyle{2}{x}=\frac{{{\log{{13}}}}}{{{\log{{11}}}}}-$
1

$\displaystyle{x}={\left(\frac{{{\log{{13}}}}}{{{\log{{11}}}}}-\right.}$
1)/2

The solution of the given equation is x = $\displaystyle{\left({\left({\log{}}\right.}\right.}$
13)/(log 11) - 1)/2

Notes