welders log question

Question

Welders use a logarithmic scale to identify protective eyewear. The shade number, n, is given by the equation

n=1-(7logT)/3, where T is the fraction of visible light that the glass transmits.

 

a. Viewing a solar eclipse through #14 welding glasses is considered safe. What fraction of light do these glasses transmit?

 

b. For doing furnace repairs, #2 welding glasses are sufficient. How many times as much visible light is transmitted by #2
welding glasses as by #14 welding glasses?

 

How do get an answer of approximately 138950 times as much for part b.? 

Answer 1

Ed,

 

Solving your formula for Log T, I get:      Log T = 3(n-1)/(-7)

 

For (a):   Log T = -39/7 = - 5.57143 ,  so for N=#14       T = 2.682696 x 10^-6 .

 

For (b):   Log T = -3/7 = -0.4285714,  so for N=#2         T = 0.3727594

 

   T-Ratio of #2/#14 =  0.3727594 / 2.682696 x 10-6  = 0.13895 x 10+6  =  138,950