Question

Solve the following logarithmic equation: log subscript 10 (5x) = 3

Answer 1

To solve the logarithmic equation log10 (5x) = 3, convert it to the exponential form 10^3 = 5x, calculate 10^3 which is 1000, and then divide by 5 to find that x equals 200.

Step-by-step explanation:

To solve the given logarithmic equation log10 (5x) = 3, we need to understand that logarithms represent the power to which a base number must be raised to obtain a certain value. In this case, the base number is 10. The equation tells us that 10 must be raised to the power of 3 to equal 5x.

To find the value of x, we use the property of logarithms that states the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. Since logarithms and exponentials are inverse functions, we can re-write the equation in exponential form to isolate x.

Following these steps:

1. Convert the logarithmic equation to an exponential equation: 103 = 5x.
2. Calculate 10 raised to the power of 3: 103 = 1000.
3. Divide both sides of the equation by 5 to solve for x: x = 1000 / 5.
4. Simplify the equation to find the value of x: x = 200.