Solve for x by using log. Rounded to hundredth. [tex]4^{2x-5} =6^{-x+1}[/tex]
Accepted Solution
A:
Answer: [tex]x=1.91[/tex]Step-by-step explanation: Given the expression [tex]4^{2x-5} =6^{-x+1}[/tex], apply logarithm to both sides. Then: [tex]log(4)^{2x-5} =log(6)^{-x+1}[/tex] Remembert that according the the properties of logarithms: [tex]log(a)^n=nlog(a)[/tex] Then: [tex](2x-5)log(4)=(-x+1)log(6)[/tex] Appy distributive property and solve for "x": [tex]2xlog(4)-5log(4)=-xlog(6)+log(6)\\2xlog(4)+xlog(6)=log(6)+5log(4)\\x(2log(4)+log(6))=log(6)+5log(4)\\\\x=\frac{log(6)+5log(4)}{2log(4)+log(6)}\\\\x=1.91[/tex]