Question

Solve. log2(7x+1)=log2(2-x)

Answer 1

`\log _(10)\left(2\right)\left(7x+1\right)=\log _(10)\left(2\right)\left(2-x\right)`
Expand:

`7x\log _(10)\left(2\right)+\log _(10)\left(2\right)=2\log _(10)\left(2\right)-x\log _(10)\left(2\right)`

`7x\log _(10)\left(2\right)=-x\log _(10)\left(2\right)+\log _(10)\left(2\right)`

`8x\log _(10)\left(2\right)=\log _(10)\left(2\right)`

`(8x\log _(10)\left(2\right))/(8\log _(10)\left(2\right))=(\log _(10)\left(2\right))/(8\log _(10)\left(2\right))`
So:

`x=(1)/(8)`

Answer 2

7x+1=2-x
The answer is x=1/8