Solve the equation:

\[
\log_8(2-5x) = \log_8(-4x+3)
\]

2 - 5x > 0 and -4x + 3> 0
log8(2-5x)=log8(-4x+3) <=> 2 - 5x = - 4x + 3 <=> -5x + 4x = 3 - 2 <=> -x = 1 <=> x = -1; 2 - 5(-1) = 7 > 0 and -4(-1) + 3 = 7 > 0 ;
the solution is -1;

Answered by crisforp | 2024-06-10

To solve the equation lo g 8 ​ ( 2 − 5 x ) = lo g 8 ​ ( − 4 x + 3 ) , we equate the arguments and solve for x . The solution is x = − 1 , which satisfies the conditions for both logarithmic arguments being positive. Therefore, the valid solution is x = − 1 .
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Answered by crisforp | 2024-12-20