Express ^@(log _a \space x)(log _b \space a)^@ as a single logarithm.


^@log _b \space x^@

Step by Step Explanation:
  1. According to the change of base formula of logarithm, ^@log _b \space m = \dfrac{ log _a \space m } { log _a \space b }^@
  2. We can write ^@(log _a \space x)^@ as ^@\dfrac{ log _b \space x }{ log _b \space a } ^@
  3. ^@(log _a \space x)(log _b \space a) ^@^@= \left( \dfrac{ log _b \space x } { log _b \space a } \right) (log _b \space a)^@
    ^@\implies (log _a \space x)(log _b \space a) = log _b \space x.^@
    Hence, ^@(log _a \space x)(log _b \space a) ^@ as a single logarithm is ^@log _b \space x^@.

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