Solve for x:
log(x)/log(4)+log(x)/log(16)==4.5
4.5==9/2:
log(x)/log(4)+log(x)/log(16)==9/2
Rewrite the left hand side by combining fractions. log(x)/log(4)+log(x)/log(16) == ((log(4)+log(16)) log(x))/(log(4) log(16)):
((log(4)+log(16)) log(x))/(log(4) log(16))==9/2
Divide both sides by log(4)+log(16)/(log(4) log(16)):
log(x)==(9 log(4) log(16))/(2 (log(4)+log(16)))
Cancel logarithms by taking exp of both sides:
x==E^((9 log(4) log(16))/(2 (log(4)+log(16))))
x = 64
