Question

Solve for x, exact answer using either base-10 or base-e logarithms

Answer 1

`13^(-x+6)=12^(-4x)`

If this equation is valid, then the following equation must also be valid:

`\begin{gathered} \log _(10)13^(-x+6)=\log _(10)12^(-4x) \\ (-x+6)\cdot\log _(10)13=-4x\cdot\log _(10)12 \\ -x\cdot\log _(10)13+6\log _(10)13+4x\log _(10)12=0 \\ x(4\log _(10)12-\log _(10)13)=-6\log _(10)13 \\ x(\log _(10)(12^4)/(13))=-6\log _(10)13 \\ x=(-6\log _(10)13)/((\log _(10)(12^4)/(13))) \end{gathered}`