Question

How to solve log(-2x+9)=log(7-4x)?

Answer 1

`x=-1`

Explanation:

Both sides involve the common logarithm. The terms in the parentheses will be equal to one another.

When we have an equation `logx=logy,` we can say `x=y.`

Thus,

`-2x+9=7-4x`

`-2x+4x=7-9`

`2x=-2, x=-1`

Check the solution to ensure it does not result in negative arguments for the logarithms on either side, as logarithms of negative numbers do not exist.

`log(-2*-1+9)=log(7-(4*-1)) hArr log(11)=log(11)`

The solution is valid.

Answer 2

`x=-1`

Explanation:

`"using the "color(blue)"law of logarithms"`

`•color(white)(x)log_b x=log_byhArrx=y`

`rArr-2x+9=7-4x`

`rArr-2x+4x=7-9`

`rArr2x=-2rArrx=-1`