Question 736028
Solve for x:log 16 base x÷log x base 16=3
{{{log(x,(16))/log(16,(x))=(3)}}}
Convert to base(10)
{{{(log(16)/log(x))/(log(x)/log(16))=(3)}}}
{{{((log(16))^2)/((log(x))^2)=(3))}}}
take sqrt of both sides:
{{{(log(16))/(log(x))=sqrt(3))}}}
log(16)=√3log(x)
log(x)=log(16)/√3≈0.6952
x=10^0.6962≈4.9568
..
Check:
log(16) basex≈1.732
logx base(16)≈0.5773
(1.732/0.5773≈2.999..≈3