Solve the equation. Round to the nearest hundredth. Show work.[tex]8^{-x+7} = 3^{7x+2}[/tex]

Answer:Final answer is approx x=1.27.Step-by-step explanation:Given equation is [tex]8^{-x+7}=3^{7x+2}[/tex].Now we need to solve equation [tex]8^{-x+7}=3^{7x+2}[/tex] and round to the nearest hundredth. [tex]8^{-x+7}=3^{7x+2}[/tex][tex]\log(8^{-x+7})=\log(3^{7x+2})[/tex][tex]\left(-x+7\right)\cdot\log\left(8\right)=\left(7x+2\right)\cdot\log\left(3\right)[/tex][tex]-x\cdot\log\left(8\right)+7\cdot\log\left(8\right)=7x\cdot\log\left(3\right)+2\cdot\log\left(3\right)[/tex][tex]-x\cdot\log\left(8\right)-7x\cdot\log\left(3\right)=2\cdot\log\left(3\right)-7\cdot\log\left(8\right)[/tex][tex]x\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)=\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)[/tex][tex]x=\frac{\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)}{\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)}[/tex]Now use calculator to calculate log values, we get:[tex]x=1.26501646392[/tex]Round to the nearest hundredth. Hence final answer is approx x=1.27.