Question

91. Solve each equation. Express your answer as a logarithm, and then approximate the solution to the nearest thousandth.

a. 3(10)−x = 1/9

Answer 1

Given :

`3*(10)^(-x) = (1)/(9)`

Therefore, taking log on both sides we get:

`log(3*(10)^(-x)) = log((1)/(9))`

`log(3) - x* log(10) = log(1) - log(9)`

Now, equating the values of the above variables we get:

0.4771 - x(1) = 0 - 0.9542

x = 0.4771 + 0.9542

x = 1.4313