Question

Resolva em IR as equações

Log na Base 3 (5x-6)=2

Log na Base 7 (9x-1) = Log na Base 7 (4-2x)

Answer 1

3^2 = 5x-6
9= 5x-6
5x= 15
x=3

9x-1=4-2x
11x= 5
x=0.45 (essa última eu tô com dúvida)

Answer 2

$log_{3} (5x-6) = 2$
3² = 5x-6
5x-6 = 3²
5x-6 = 9
5x = 9+6
5x = 15
x = 15/5
x = 3

C.E.: 5x-6>0
5x>6
x>6/5
x>1,2

$log_{7} (9x-1) = log_{7} (4-2x)$
9x-1 = 4-2x
9x+2x = 4+1
11x = 5
x= 5/11

C.E.: 9x-1>0
9x>1
x>1/9

4-2x>0
-2x>-4.(-1)
2x<4
x<4/2
x<2

2>x>1/9