Question

Solve for x. Show work. Show result to three decimal places

Answer 1

`3^(x+1)=8^x\implies 3^x\cdot 3=8^x\implies 3=\cfrac{8^x}{3^x}\implies 3=\left( \cfrac{8}{3} \right)^x \\\\\\ \log(3)=\log\left[\left( \cfrac{8}{3} \right)^x \right]\implies \log(3)=x\log\left[\left( \cfrac{8}{3} \right) \right] \\\\\\ (\log(3))/( ~~ \log\left( (8)/(3) \right) ~~ )=x\implies 1.120\approx x`

Answer 2

`3^(x+1)=8^x\\\log3^(x+1)=\log8^x\\(x+1)\log 3=x\log 8\\x\log 3+\log 3=x\log 8\\x\log8-x\log 3=\log 3\\x(\log 8 -\log 3)=\log 3\\x=(\log3)/(\log 8-\log3)=(\log 3)/(\log\left((8)/(3)\right))\approx1.12`