2^x3=3^x^2
Follow Math Help Forum on Facebook and Google+
Originally Posted by alessandromangione 2^x3=3^x^2 This is near impossible to read. Is it $\displaystyle 2^{x^3} = 3^{x^2}$?
yeap...sorry...
$\displaystyle 2^{x^3} = 3^{x^2}$ $\displaystyle \ln{\left(2^{x^3}\right)} = \ln{\left(3^{x^2}\right)}$ $\displaystyle x^3\ln{2} = x^2\ln{3}$ $\displaystyle \frac{x^3}{x^2} = \frac{\ln{3}}{\ln{2}}$ $\displaystyle x = \frac{\ln{3}}{\ln{2}}$.
Hello everyone Don't forget that there's another solution to the equation $\displaystyle x^3\ln2 =x^2\ln3$ besides $\displaystyle x=\frac{\ln3}{\ln2}$, and that is $\displaystyle x=0$ Grandad
View Tag Cloud