Question

For positive number of a, k, T and S where neither 'a' nor 'S' equals unity, if $\left({\log }_{s}a\right)\left(a^{{\log }_{a}k}\right)=1-\left({\log }_{S}a\right)\left({\log }_{a}T\right)$ then S equals -

• A. $T{a}^k$
• B. $Tk$
• C. $T{a}^{-k}$
• D. $T-a^k$

Answer 1

Answer: (A)

$T{a}^k$

Given

$\left(lo{g}_{s}a\right)\left(a^{lo{g}_{a}k}\right)=1-\left(lo{g}_{s}a\right)\left(lo{g}_{a}T\right)$

$lo{g}_{s}a\left(k\right)=1-\frac{loga}{logS}\frac{logT}{loga}$

$\frac{loga}{logS}k=1-\frac{logT}{logS}$

$\frac{loga}{logS}k=\frac{logs-logT}{logS}$

$kloga=logS-logT$

$log{a}^k+logT=logS$

$log(a^k.T)=logS$

$S=a^k.T$