logarithims

[Susan Symonds]

can anyone solve this, please?

3^(2x+3)=2^(2-3x)

I have been fighting with it for 2 days!

Thanks

 

[pka]

$\displaystyle {\rm{3}}^{{\rm{2x + 3}}} = 2^{2 - 3x}$

$\displaystyle \left( {2x + 3} \right)\ln (3) = \left( {2 - 3x} \right)\ln (2)$

$\displaystyle \left[ {2\ln (3) + 3\ln (2)} \right]x = 2\ln (2) - 3\ln (3)$

Now you solve for x.