How do you solve #3^x=2^(x-1)#?

Question

1828 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-16T12:37:57

#color(blue)(x~~-1.709511290)#

#3^x=2^(x-1)#

Taking logarithms of both sides:

#xln(3)=(x-1)ln(2)#

#xln(3)=xln(2)-ln(2)#

#xln(3)-xln(2)=-ln(2)#

Factor:

#x(ln(3)-ln(2))=-ln(2)#

#x=(-ln(2))/(ln(3)-ln(2))~~-1.709511290#

#color(blue)(x~~-1.709511290)#