Question

What is the solution to the equation log(2x — 7) = log(5х + 2)?
NEEED ANSWER ASAP

Answer 1

"No Solution"

Explanation:

We can use the log property shown below to simplify this:

`Log(a)=Log(b)\\Means\\a=b`

Since no "base" is given, we take base as "10" and use property to write:

`2x-7=5x+2`

Now, we solve for x:

`2x-7=5x+2\\5x-2x=-7-2\\3x=-9\\x=-3`

But we are NOT done. We have to take the value and put it into the equation to check if there is any NEGATIVE value, because we cannot take negative log.

Putting in LHS:

Log(2x - 7)

Log(2(-3) - 7)

Log(-6-7)

Log(-13)

This can't be solved. So x = -3 is not a solution. Thus, there is NO SOLUTION to the equation given.