Question

Find a rational number which is 50 times its own logarithm to the base 10.

Answer 1

solution:
let, x be rational no.
according to the question, x = 50 × log10 X
x = 100

Answer 2

The solution is 100. Just write the equation:

x=50logx

For x=1 you have 1=50×0 which is false.

For x=10 you have 10=50×1 which is false.

For x=100 you have 100=50×2 which is true.

For x=1000 you have 1000=50×3 which is false.

If you don't want to check the options the general way to solve this equation is:

x=50lnxln10

xlnx=50ln10

lnxx=ln1050

e−lnxlnx=ln1050

−e−lnxlnx=−ln1050

Now you apply Lambert's W function which is defined as W(z)eW(z)=z

−lnx=W(−ln1050)

x=e−W(−ln1050)