Negative fractional indices equations

Vikash

Junior Member
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Sep 29, 2020
Messages
62
My question is...if we have an equation like this (-2/3)x=-5 then can we take (-2/3)x to the other side and rewrite the equation as (2/3)x=5 OR NOT?? thanks....
 
My question is...if we have an equation like this (-2/3)x=-5 then can we take (-2/3)x to the other side and rewrite the equation as (2/3)x=5 OR NOT?? thanks....
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.
 
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.
Thank you so much????
 
This is not just a matter of "negative fractional indices"! You never, never, never "move to other side of the equation"! Two darn many times have I seen students "solve" a simple equation like "ax= b" as
x=-ab" saying that "my teacher said that when you move something to the other side of the equation you change the sign"!

"Moving" something is not a mathematical operation. You can add or subtract something from both sides of an equation, or multiply or divide both sides of an equation by something or even take the same power of both sides but those are all different operations that are done for a specific purpose!

To solve "ax= b" you do NOT think "move a to the other side of the equation" automatically without thinking. You think "x is not alone because it is multiplied by a. To get x alone, I need to do the opposite of multiplying- I need to divide both sides by a"!
 
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