Please help me solve these two questions:
1.) $\displaystyle 2 ln(x-1) - 2 ln(x) = 0$
2.) $\displaystyle 6^{5x+3} = 2^{x-2}$
Your assistance is greatly appreciated.
1.)
$\displaystyle 2~ln(x - 1) - 2~ln(x) = 0$
[tex]ln((x - 1)^2) - ln(x^2) = 0
$\displaystyle ln((x - 1)^2) = ln(x^2)$
$\displaystyle (x - 1)^2 = x^2$
etc.
2.)
$\displaystyle 6^{5x + 3} = 2^{x - 2}$
Take the logarithm of both sides. Any base will do. I'll use base e.
$\displaystyle ln \left ( 6^{5x + 3} \right ) = ln \left ( 2^{x - 2} \right )$
$\displaystyle (5x + 3)~ln(6) = (x - 2)~ln(2)$
etc.
-Dan