Question 919571
log(base 125)x - log(base 5)x = -2
use change of base formula:
{{{log(125,(x))=log(5,(x))/log(5,(125))=log(5,(x))/3}}}
..
{{{log(5,(x))/3-log(5,(x))=-2}}}
lcd:3
{{{log(5,(x))-3log(5,(x))=-6}}}
{{{log(5,(x/x^3))=-6}}}
5^-6=1/x^2
x^2=1/5^-6
x=±1/5^-3
x=125
check:
log(base 125)x=log(base 125)(125)=1
log(base 5)x=log(base 5)(125)=3
log(base 125)x - log(base 5)x=1-3=-2