You say:
"can we take (-2/3)x to the other side and rewrite the equation as (2/3)x=5 OR NOT??"
NO
You cannot do that.
You "switched" the "sign" inside parentheses () and that is NOT ALLOWED.
However, in this case you can ignore the sign - and check/calculate the value of 'x', by taking 'logs'. The value will be valid ONLY IF 'x' is computed to be an ODD (as opposed to EVEN) INTEGER.
For example, if you had:
(-2/3)^x = -32/243
Assuming 'x' is an 'odd integer' (we cannot assume 'x' to be even integer - why?), we calculate:
(+2/3)^x = +32/243
Now using 'log' we get
x = 5 ................ we get 'x' as an ODD integer so it is correct (assumption holds).
Another example:
For example, if you had:
(-2/3)^x = -16/81
Assuming 'x' is an 'odd integer' (we cannot assume 'x' to be even integer),
we calculate:
(+2/3)^x = +16/81
Now using 'log' we get
x = 4 ................ we get 'x' as an EVEN integer so our assumption does NOT HOLD. Hence 'x' CANNOT be calculated.