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Write the expression
ln 2+4 as a single logarithm in simplest form without any negative exponents.
Answer:
ln(◻)

Write the expression $\ln 2+4$ as a single logarithm in simplest form without any negative exponents. $\newline$ Answer: $\ln (\square)$

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Simplify radical expressions with variables

Full solution

Q. Write the expression

\ln 2+4

as a single logarithm in simplest form without any negative exponents.

\newline

Answer:

\ln (\square)

Understand Logarithm Properties: Understand the properties of logarithms The problem asks us to combine $\ln 2$ and $4$ into a single logarithm. To do this, we need to use the properties of logarithms. One of the properties is that the logarithm of a product is the sum of the logarithms ( $\log(a) + \log(b) = \log(ab)$ ). We will use this property to combine $\ln 2$ and $4$ into a single logarithm.
Convert Number $4$ to Logarithm: Convert the number $4$ into a logarithm with the same base To use the property from Step $1$ , we need to express the number $4$ as a logarithm with the same base, which is the natural logarithm (base $e$ ). We can write $4$ as $\ln(e^4)$ because the natural logarithm of $e$ to any power is just that power ( $\ln(e^x) = x$ ).
Combine Logarithms: Combine the two logarithms into one $\newline$ Now that we have both numbers as natural logarithms, we can combine them using the property from Step $1$ : $\newline$ $\ln 2 + \ln(e^4) = \ln(2 \cdot e^4)$
Simplify Expression: Simplify the expression The expression $\ln(2 \cdot e^4)$ is already in its simplest form. There are no negative exponents, and it is written as a single logarithm.

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