Verified answer

For |a| ≠ |b|,

a^x = b^x

ln(a^x) = ln(b^x)

xln(a) = xln(b)

xln(a) - xln(b) = 0

x(ln(a) - ln(b)) = 0

x = 0

For a = -b, x ∈ 2Z.

For a = b, x ∈ R.

(1/9)^x ≥ (2/3)^x

ln((1/9)^x) ≥ ln((2/3)^x)

xln(1/9) ≥ xln(2/3)

xln(1/9) - xln(2/3) ≥ 0

x(ln(1/9) - ln(2/3)) ≥ 0

x ≤ 0 [the sign was flipped because ln(1/9) - ln(2/3) < 0]

Your first example is impossible since

(1/9)^x cannot = (6/9)^x, however the

second quantity is obviously larger (>)

Use logic and equate the expressions

to compare them.

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