Find the value of the question mark. *

-2m - 3n

Step-by-step explanation:

a(m+n)/a(−2n−m) = 1/ax  

Rewrite the equation as  1/ax  = am+n/a−2n−m.

1/ax = am+n/a−2n−m

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

ln( 1/ax  ) = ln ( am+n/a^{−2n−m})

Expand the left side.

−x ln(a) = ln (am+n/a^{−2n−m})

Expand the right side.

−x ln (a) = (m + n) ln (a) − (−2n − m) ln (a)

Simplify (m + n) ln (a) − (−2n − m) ln (a).

−x ln (a) = 2m ln (a) + 3n ln (a)

Move all the terms containing a logarithm to the left side of the equation.

−x ln (a) −2m ln (a) − 3n ln (a) = 0

Move all terms not containing x to the right side of the equation.

−x ln (a) = 2m ln (a) + 3n ln (a)

Divide each term by −1 ln (a) and simplify.

x  = −2m − 3n

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