The expression a a( log ( log a)/ log a) where all logarithm are taken to the base b is equal to

Question

The expression a a( log ( log a)/ log a) where all logarithm are taken to the base b is equal to (A)  log a a b (B)  log a b (C)  log b a (D)  log b ab -1

Tardigrade Admin · Accepted Answer

a log b ( log b a ) ⋅ log a b text Let log b a = m a log b m ⋅ log a b = a log a m ⇒ m = log b a

Q. The expression a $a^{\frac{l o g ( l o g a )}{l o g a}}$ where all logarithm are taken to the base b is equal to

$lo g_{a} ab$

$lo g_{a} b$

$lo g_{b} a$

$lo g_{b} ab - 1$

$a^{l o g_{b} (l o g_{b} a) \cdot l o g_{a} b}$
$Let lo g_{b} a = m$
$a^{l o g_{b} m \cdot l o g_{a} b} = a^{l o g_{a} m} \Rightarrow m = lo g_{b} a$

Q. The expression a alogalog(loga)​ where all logarithm are taken to the base b is equal to

loga​ab

loga​b

logb​a

logb​ab−1