Question 130626
{{{5*6^(2x-3)+1=8}}} Start with the given equation



{{{5*6^(2x-3)=7}}} Subtract 1 from both sides



{{{6^(2x-3)=7/5}}} Divide both sides by 5



{{{log(10,(6^(2x-3)))=log(10,(7/5))}}} Take the log of both sides



{{{(2x-3)log(10,(6))=log(10,(7/5))}}} Rewrite the left side using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}



{{{2x-3=log(10,(7/5))/log(10,(6))}}} Divide both sides by {{{log(10,(6))}}}



{{{2x-3=log(6,(7/5))}}} Now use the change of base formula to simplify {{{log(10,(7/5))/log(10,(6))}}} to get {{{log(6,(7/5))}}}



{{{2x=log(6,(7/5))+3}}}  Add 3 to both sides




{{{x=(log(6,(7/5))+3)/2}}} Divide both sides by 2 to isolate x