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

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

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

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

View step-by-step help

Home

Math Problems

Algebra 2

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: $64 \times e^2$