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

Apply Logarithm Property: Apply the property of logarithms that allows us to move the coefficient in front of the logarithm to the exponent inside the logarithm. Property: a * ln(b) = ln(b^a) Calculation: 2ln(4) becomes ln(4^2) Math error check: Simplify Inside Logarithm: Simplify the expression inside the logarithm. Calculation: 4^2 = 16 Math error check: Rewrite Using Simplified Logarithm: Rewrite the expression using the simplified logarithm. Calculation: e^(ln(16) - 3) Math error check: Apply Exponent Property: Apply the property of logarithms and exponents that states e^(ln(x)) = x. Property: e^(ln(x)) = x Calculation: e^(ln(16)) = 16 Math error check: Combine Exponential and Constant Terms: Simplify the expression by combining the exponential and constant terms. Calculation: 16 * e^(-3) Math error check: Calculate Constant: Recognize that e^(-3) is a constant that can be calculated. Calculation: e^(-3) ≈ 0.0498 (rounded to four decimal places) Math error check: Multiply to Get Final Answer: Multiply the constant e^(-3) by 16 to get the final answer. Calculation: 16 * 0.0498 ≈ 0.7968 (rounded to four decimal places) Math error check:

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

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

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Precalculus

Power property of logarithms

Full solution

Q. Simplify

e^{2 \ln 4-3}

and write without any logarithms.

\newline

Answer:

Apply Logarithm Property: Apply the property of logarithms that allows us to move the coefficient in front of the logarithm to the exponent inside the logarithm. $\newline$ Property: $a \cdot \ln(b) = \ln(b^a)$ $\newline$ Calculation: $2\ln(4)$ becomes $\ln(4^2)$ $\newline$ Math error check:
Simplify Inside Logarithm: Simplify the expression inside the logarithm. $\newline$ Calculation: $4^2 = 16$ $\newline$ Math error check:
Rewrite Using Simplified Logarithm: Rewrite the expression using the simplified logarithm. $\newline$ Calculation: $e^{\ln(16) - 3}$ $\newline$ Math error check:
Apply Exponent Property: Apply the property of logarithms and exponents that states $e^{\ln(x)} = x$ . $\newline$ Property: $e^{\ln(x)} = x$ $\newline$ Calculation: $e^{\ln(16)} = 16$ $\newline$ Math error check:
Combine Exponential and Constant Terms: Simplify the expression by combining the exponential and constant terms. $\newline$ Calculation: $16 \times e^{-3}$ $\newline$ Math error check:
Calculate Constant: Recognize that $e^{-3}$ is a constant that can be calculated. $\newline$ Calculation: $e^{-3} \approx 0.0498$ (rounded to four decimal places) $\newline$ Math error check:
Multiply to Get Final Answer: Multiply the constant $e^{-3}$ by $16$ to get the final answer. $\newline$ Calculation: $16 \times 0.0498 \approx 0.7968$ (rounded to four decimal places) $\newline$ Math error check: