Answer: -2m - 3n
Step-by-step explanation:
a(m+n)/a(−2n−m) = 1/ax
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<u>Rewrite the equation as 1/ax = am+n/a−2n−m.</u>
1/ax = am+n/a−2n−m
<u>Take the natural logarithm of both sides of the equation to remove the variable from the exponent.</u>
ln( 1/ax ) = ln ( am+n/a^{−2n−m})
<u>Expand the left side.</u>
−x ln(a) = ln (am+n/a^{−2n−m})
<em><u>Expand the right side.</u></em>
−x ln (a) = (m + n) ln (a) − (−2n − m) ln (a)
<u>Simplify (m + n) ln (a) − (−2n − m) ln (a).</u>
−x ln (a) = 2m ln (a) + 3n ln (a)
<u>Move all the terms containing a logarithm to the left side of the equation.</u>
−x ln (a) −2m ln (a) − 3n ln (a) = 0
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<u>Move all terms not containing x to the right side of the equation.</u>
−x ln (a) = 2m ln (a) + 3n ln (a)
<u>Divide each term by −1 ln (a) and simplify.</u>
x = −2m − 3n
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