Question

10 In(100x) – 3 = 117​

Answer 1

To solve the equation 10 ln(100x) - 3 = 117, first isolate the ln(100x) by adding 3 to both sides and then divide by 10. Exponentiate both sides with base e to remove the ln, and finally divide by 100 to solve for x.

Step-by-step explanation:

Solve the logarithmic equation

We are given the equation 10 ln(100x) – 3 = 117. To solve for x, follow these steps:

1. Add 3 to both sides of the equation to isolate the logarithmic expression.
   

   10 ln(100x) = 120

2. Divide both sides by 10 to isolate ln(100x).
   

   ln(100x) = 12

3. To remove the natural log, we exponentiate both sides with base e.
   

   100x = e^12

4. Divide both sides by 100 to solve for x.
   

   x = (e^12) / 100

Now, by using a calculator we can find the value of e^12 and then divide it by 100 to find the value of x.

Final answer is: x = 1627.54

Answer 2

x = e^12/100

Step-by-step explanation:

Solve for x over the real numbers:

10 ln(100 x) - 3 = 117

Add 3 to both sides:

10 ln(100 x) = 120

Divide both sides by 10:

ln(100 x) = 12

Cancel logarithms by taking exp of both sides:

100 x = e^12

Divide both sides by 100:

Answer: x = e^12/100