LOGARITHMS 6

If Log[(30x-70)/(5+x)] = 1. Find x.

Solution

Log[(30x-70)/(5+x)] = 1.

Log₁₀[(30x-70)/(5+x)] = 1.

 30x-70 = 10¹. After changing into exponential form

   5+x

30x-70 = 10    since [10¹=10]

   5+x

30x-70 = 10(5+x)    after cross multiply

  

30x-70 = 50+10x

30x-10x = 50+70 [collecting like terms]

20x = 120

x=6  [after dividing by 20 both sides]

Hence x=6.

TRY THIS……………

If Log[(2x+4)/(x-2)] = 1. Find x.