solve the equation 3(2^(x-3))=6^(x-1)

Question

jhonyy9 · Answer

idea ? opinion ?

anonymous · Answer

idea

jhonyy9 · Answer

courage 

how we can solving the same equations when x is on the exponent ?

kirbykirby · Answer

^this mean's it's a candidate to use logarithms, since logarithms bring the exponent down

anonymous · Answer

how to eliminate the 3 in front of 2^(x-3) ?

kirbykirby · Answer

I'm trying to do it on paper. I'll get back to u in a few

kirbykirby · Answer

Ok got it. Give me some time to write it up

anonymous · Answer

ok

kirbykirby · Answer

$$3(2^{x-3})=6^{x-1}$$
$ln(3(2^{x-3}))=ln(6^{x-1})$                               by taking ln on both sides 
$ln(3)+ln(2^{x-3})=ln(6^{x-1})$                        using log rule $ln(a*b)=ln(a)+ln(b)$
$ln(3)+(x-3)ln(2)=(x-1)ln(6)$              by using log rule $ln(a^b)=b*ln(a)$
$ln(3)+x*ln(2)-3ln(2)=x*ln(6)-ln(6)$  distributivity
$x*ln(6)-x*ln(2)=ln(3)-3ln(2)+ln(6)$      bring all x terms to one side
$x[ln(6)-ln(2)]=ln(3)-3ln(2)+ln(6)$           factor out x
$$x=\frac{ln(3)-3ln(2)+ln(6)}{ln(6)-ln(2)}$$

kirbykirby · Answer

$$3(2^{x-3})=6^{x-1}$$
$ln(3(2^{x-3}))=ln(6^{x-1})$                               by taking ln on both sides 
$ln(3)+ln(2^{x-3})=ln(6^{x-1})$              using log rule $ln(a*b)=ln(a)+ln(b)$
$ln(3)+(x-3)ln(2)=(x-1)ln(6)$              by using log rule $ln(a^b)=b*ln(a)$
$ln(3)+x*ln(2)-3ln(2)=x*ln(6)-ln(6)$  distributivity
$x*ln(6)-x*ln(2)=ln(3)-3ln(2)+ln(6)$      bring all x terms to one side
$x[ln(6)-ln(2)]=ln(3)-3ln(2)+ln(6)$           factor out x
$$x=\frac{ln(3)-3ln(2)+ln(6)}{ln(6)-ln(2)}$$

kirbykirby · Answer

ok hopefully that's a bit more clear, my line got shifted down

anonymous · Answer

thanks

kirbykirby · Answer

in decimal it's about 0.73814