Question

Logarithmic and Exponential Forms of Equations In Exercise, write the logarithmic equation as an exponential equation, or vice versa.

e1.5 = 4.4816 ...

Answer 1

`\log_e(4.4816) = 1.5`

Explanation:

We are given the following in the question:

`e^(1.5) = 4.4816...`

We have to convert this equation into logarithmic equation.

Relation between exponent and logarithmic:

• Logarithmic functions are the inverses of exponential functions.

• The logarithmic function
  `y = \log_ax` is defined to be equivalent to the exponential equation
  `x = a^y`

For the given expression a = e, y = 1.5 and x = 4.4816...

We can express them as:

`e^(1.5) = 4.4816...\\\text{Taking log on both sidses}\\\log(e^(1.5)) = \log(4.4816)\\\log_e(4.4816) = 1.4998 \approx 1.5\\\log_e(4.4816) = 1.5`