Question 1206690
<pre>
{{{log(2,x) + log(4,x) + log(16,x) = 21/4}}}
find x. 

{{{matrix(1,2,Let, x = 16^y)}}}

{{{log(2,16^y) + log(4,16^y) + log(16,16^y) = 21/4}}}

{{{y*log(2,16) + y*log(4,16) + y*log(16,16) = 21/4}}}

{{{y*log(2,2^4) + y*log(4,4^2) + y*log(16,16) = 21/4}}}

Since {{{log(a,a^n) = n}}},

{{{4y+2y+1y=21/4}}}

{{{7y=21/4}}}

{{{y=3/4}}}

{{{x=16^y=16^("3/4")=(2^4)^("3/4")= 2^3=8}}}

Edwin</pre>