Question

log2(8-x)=5
log3(8-x)=3
log2(x 3)=log2(3x-15)
log8(x 4)=log8(5x-16)

Answer 1

1) 
$displaystyle log_2(8-x)=5\\ODZ: 8-x textgreater 0; x textless 8\\8-x=2^5\\x=8-32\\x=-24$

2) 
$displaystyle log_3(8-x)=3\\ODZ: x textless 8\\8-x=3^3\\x=8-27\\x= -19$

3) 
$displaystyle log_2(x-3)=log_2(3x-15)\\ODZ: left { {{x-3 textgreater 0} atop {3x-15 textgreater 0}} right.: left { {{x textgreater 3} atop {x textgreater 5}} right. ; X textgreater 5\\x-3=3x-15\\12=2x\\x=6$

4) 
$displaystyle log_8(x-4)=log_8(5x-16)\\ODZ: left { {{x-4 textgreater 0} atop {5x-16 textgreater 0}} right.; left { {{x textgreater 4} atop {x textgreater 16/5}} right. ; X textgreater 4\\x-4=5x-16\\12=4x\\x=3$

нет решений