Question 167773
{{{2^(3x-1)=7^(x-q)}}} Start with the given equation



{{{ln(2^(3x-1))=ln(7^(x-q))}}} Take the natural log of both sides. This step is needed since the variable we want to solve for is in the exponent.




{{{(3x-1)ln(2)=(x-q)ln(7)}}} Rewrite the left side using the identity  {{{ln(x^y)=y*ln(x))}}}




{{{3x*ln(2)-ln(2)=x*ln(7)-q*ln(7)}}} Distribute



{{{3x*ln(2)-x*ln(7)=-q*ln(7)+ln(2)}}} Subtract {{{x*ln(7)}}} from both sides. Add {{{ln(2)}}} to both sides.



{{{3x*ln(2)-x*ln(7)=ln(2)-q*ln(7)}}} Rearrange the terms on the right side



{{{x(3*ln(2)-ln(7))=ln(2)-q*ln(7)}}} Factor out the GCF "x" from the left side.



{{{x=(ln(2)-q*ln(7))/(3*ln(2)-ln(7))}}} Divide both sides by {{{3*ln(2)-ln(7)}}} to isolate "x"



So the solution is {{{x=(ln(2)-q*ln(7))/(3*ln(2)-ln(7))}}}