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