Alg9.4.15

Find the value of x if $\log_\sqrt{2}(\log_2(\log_2(x-15))=0\,$

Applying the basic logarithmic principle to the given equation,

$\log_2(\log_2(x-15))=(\sqrt{2})^{0}\,$

$\log_2(\log_2(x-15))=1\,$

Again applying the basic principle,we get

$\log_2(x-15)=2^1\,$

$x-15=2^2\,$

Hence

$x=19\,$

The value of x is 19