Question

Simplify each expression. ln e3 = ln e2y =

Answer 1

Answer:

$ln\hspace{1mm} e^3=3$, $ln\hspace{1mm} e^{2y}=2y$

Step-by-step explanation:

We know that $ln \hspace{1mm} e =log_e e= 1$ and according to power rule:

$ln(x^y) = y ln(x)$

Thus,

$ln\hspace{1mm}e^3=3 ln\hspace{1mm} e =3$

$ln\hspace{1mm}e^{2y}=2y ln\hspace{1mm} e = 2y$

Answer 2

The expressions of log equations can modify by using the properties of the log.

The simplified expressions are $In\;e^3 = 3 In\;e$ and $In\;e^{2y} = 2y In\;e$.

How do you simplify the logarithm expression?

The four basic properties of Logs are given below.

$log_b (xy) = log_b x + log_b y.$

$log_b (\dfrac {x}{y}) = log_b x - log_b y.$

$log_b (x^n) = n log_b x.$

$log_b x = \dfrac {log_a x}{ log_a b}$

The given expression is $ln \;e^3$ and $In\;e^{2y}$.

The above expressions of the logarithm can be solved by using the third property of log.

Part A:

The expression of the logarithm is $In\;e^3$.

This can be written as using one of the properties of the log.

$In\;e^3 = 3 In\;e$

Part B:

The expression of the logarithm is $In\;e^{2y}$.

This can be written as using one of the properties of the log.

$In\;e^{2y} = 2y In\;e$

Hence we can conclude that the expressions of log equations can modify by using the properties of the log.

The simplified expressions are $In\;e^3 = 3 In\;e$ and $In\;e^{2y} = 2y In\;e$.

To know more about the logarithm, follow the link given below.

https://brainly.com/question/7302008.