Question

If $y={\left(a^x\right)}^{{\left(a^x\right)}^{{.}^{{.}^{{.}^{.}}\infty }}}$, then which one of the following is correct?

• A. $\log y=xy\log a$
• B. $\log y=x+y\log a$
• C. $\log y=y+x\log a$
• D. $\log y=(x+y)\log a$

Answer 1

The correct option is A $\log y=xy\log a$

Given,

$y=(a^x{)}^{(a^x{)}^{........\infty }}$

From given, we have,

$y=(a^x{)}^y$

$y=a^{xy}$

taking $\log$ on both sides, we have,

$\log y=\log a^{xy}$

$\log y=xy\log a$