To convert the exponential equation e5x = 4768 into its logarithmic form, we follow the definition of logarithms. The exponential equation states that e raised to the power of 5x equals 4768. In logarithmic terms, we express this relationship as:
5x = ln(4768)
Here’s how we arrive at this: The logarithmic form of an equation by = x can be expressed as y = logb(x). In our case:
- b is e, the base of natural logarithms.
- y is 5x.
- x is 4768.
This means we can write the equation as:
5x = ln(4768)
To isolate x, we can divide both sides by 5:
x = (1/5) * ln(4768)
This gives us the final value of x in terms of the natural logarithm of 4768. Therefore, the logarithmic form of the equation e5x = 4768 is:
5x = ln(4768)