Express (loga x)(logb a)(loga x)(logb a)(loga x)(logb a) as a single logarithm.
Answer:
logb xlogb xlogb x
- According to the change of base formula of logarithm, logb m=loga mloga blogb m=loga mloga blogb m=loga mloga b
- We can write (loga x)(loga x)(loga x) as logb xlogb alogb xlogb alogb xlogb a
- (loga x)(logb a)(loga x)(logb a)(loga x)(logb a)=(logb xlogb a)(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.