log16 (x) +log4 (x) +log2 (x) =7 condense so. Condense them to the same base before solving for x

Question

Please help and show the steps so I could understand how to condense when the bases aren't the same.

Answer 1

log16(x)=(1/4)log2(x)

log4(x)=(1/2) log2(x)

so yu hav (1+1/2+1/4)log2(x)=7

1.75*log2(x)=7

log2(x)=7/1.75=4

x=2^4=16

Answer 2

 Log16x + log4x + log2x = 7 
use change of base formula 
logx/log16 + logx/log4 + logx/log2 = 7 
logx/log(2^4) + logx/log(2^2) + logx/log2 = 7 
logx/4log2 + logx/2log2 + logx/log2 = 7 
logx/log2 * (1/4 + 1/2 + 1) = 7 
logx/log2 * (7/4) = 7 
logx/log2 * (1/4) = 1 
logx/log2 = 4 
logx = 4log2 
logx = log(2^4) 
x = 2^4 = 16