Answer
see an explanation
Work Step by Step
a. $3^{4x}=3^{100}$,
$4x=100$,
$x=25$
b. $e^{3x-2}=e^{x^2}$,
$3x-2=x^2$,
$x^2-3x+2=0$,
$x^2-x-2x+2=0$,
$x(x-1)-2(x-1)=0$,
$(x-2)(x-1)=0$,
$x=2$ or $x=1$
c. $5^{x/10}+1=7$,
$5^{x/10}=6$,
$\frac{x}{10}\log5=\log6$,
$x=\frac{\log6\times10}{\log5}$
$x=11.13$
d. $10^{x+3}=6^{2x}$,
$x+3=2x\log6$,
$2x\log6-x=3$,
$x(2\log6-1)=3$,
$x=\frac{3}{2\log6-1}=5.39$
