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Simplify
e^(3ln 4+2) and write without any logarithms.
Answer:

Simplify $e^{3 \ln 4+2}$ and write without any logarithms. $\newline$ Answer:

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Change of base formula

Full solution

Q. Simplify

e^{3 \ln 4+2}

and write without any logarithms.

\newline

Answer:

Apply power rule of logarithms: Apply the power rule of logarithms to the term $3\ln(4)$ . The power rule states that $a \cdot \ln(b) = \ln(b^a)$ . Therefore, we can rewrite $3\ln(4)$ as $\ln(4^3)$ . Calculation: $3\ln(4) = \ln(4^3) = \ln(64)$
Rewrite using result from Step $1$ : Rewrite the original expression using the result from Step $1$ . $\newline$ The original expression is $e^{3\ln 4+2}$ . Using the result from Step $1$ , we can rewrite it as $e^{\ln(64)+2}$ . $\newline$ Calculation: $e^{\ln(64)+2}$
Use property of exponents: Use the property of exponents to separate the terms in the exponent. $\newline$ The property $e^{a+b} = e^a \cdot e^b$ allows us to separate the terms in the exponent. $\newline$ Calculation: $e^{\ln(64)+2} = e^{\ln(64)} \cdot e^2$
Simplify $e^{\ln(64)}$ : Simplify $e^{\ln(64)}$ . $\newline$ The property $e^{\ln(a)} = a$ allows us to simplify $e^{\ln(64)}$ to just $64$ . $\newline$ Calculation: $e^{\ln(64)} = 64$
Combine results from Step $3$ and Step $4$ : Combine the results from Step $3$ and Step $4$ . $\newline$ We have $e^{\ln(64)} \times e^2$ , which simplifies to $64 \times e^2$ . $\newline$ Calculation: $64 \times e^2$

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