Express (loga x)(logb a)(loga x)(logb a) as a single logarithm.


Answer:

logb xlogb x

Step by Step Explanation:
  1. According to the change of base formula of logarithm, logb m=loga mloga blogb m=loga mloga b
  2. We can write (loga x)(loga x) as logb xlogb alogb xlogb a
  3. (loga x)(logb a)(loga x)(logb a)=(logb xlogb a)(logb a)=(logb xlogb a)(logb a)
    (loga x)(logb a)=logb x.(loga x)(logb a)=logb x.
    Hence, (loga x)(logb a)(loga x)(logb a) as a single logarithm is logb xlogb x.

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