Given the substitutions ln 2=a,ln 3=b, and ln 5=c, find the value of ln((4)/(sqrt3)) in terms of a,b, and c. Answer:

Identify expression and substitutions: Identify the expression to be simplified and the given substitutions. ln((4)/(sqrt(3))) needs to be expressed in terms of a, b, and c. Given: ln(2)=a, ln(3)=b, ln(5)=c.Rewrite using logarithm properties: Rewrite the expression ln((4)/(sqrt(3))) using the properties of logarithms. ln((4)/(sqrt(3))) = ln(4) - ln(sqrt(3))Express in terms of a, b, c: Express ln(4) and ln(sqrt(3)) in terms of ln(2) and ln(3). ln(4) = ln(2^2) = 2ln(2) = 2a ln(sqrt(3)) = ln(3^(1/2)) = (1/2)ln(3) = (1/2)bSubstitute values back: Substitute the values of ln(4) and ln(sqrt(3)) back into the original expression. ln((4)/(sqrt(3))) = 2a - (1/2)bSimplify if necessary: Simplify the expression if necessary. The expression is already simplified: ln((4)/(sqrt(3))) = 2a - (1/2)b

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Given the substitutions
ln 2=a,ln 3=b, and
ln 5=c, find the value of
ln((4)/(sqrt3)) in terms of
a,b, and
c.
Answer:

Given the substitutions $\ln 2=a, \ln 3=b$ , and $\ln 5=c$ , find the value of $\ln \left(\frac{4}{\sqrt{3}}\right)$ in terms of $a, b$ , and $c$ . $\newline$ Answer:

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Algebra 1

Write variable expressions for arithmetic sequences

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Q. Given the substitutions

\ln 2=a, \ln 3=b

, and

\ln 5=c

, find the value of

\ln \left(\frac{4}{\sqrt{3}}\right)

in terms of

a, b

, and

c

\newline

Answer:

Identify expression and substitutions: Identify the expression to be simplified and the given substitutions. $\ln\left(\frac{4}{\sqrt{3}}\right)$ needs to be expressed in terms of $a$ , $b$ , and $c$ . Given: $\ln(2)=a$ , $\ln(3)=b$ , $\ln(5)=c$ .
Rewrite using logarithm properties: Rewrite the expression $\ln\left(\frac{4}{\sqrt{3}}\right)$ using the properties of logarithms. $\newline$ $\ln\left(\frac{4}{\sqrt{3}}\right) = \ln(4) - \ln(\sqrt{3})$
Express in terms of $a$ , $b$ , $c$ : Express $\ln(4)$ and $\ln(\sqrt{3})$ in terms of $\ln(2)$ and $\ln(3)$ .
$\ln(4) = \ln(2^2) = 2\ln(2) = 2a$
$\ln(\sqrt{3}) = \ln(3^{1/2}) = (1/2)\ln(3) = (1/2)b$
Substitute values back: Substitute the values of $\ln(4)$ and $\ln(\sqrt{3})$ back into the original expression. $\newline$ $\ln\left(\frac{4}{\sqrt{3}}\right) = 2a - \left(\frac{1}{2}\right)b$
Simplify if necessary: Simplify the expression if necessary. $\newline$ The expression is already simplified: $\ln\left(\frac{4}{\sqrt{3}}\right) = 2a - \left(\frac{1}{2}\right)b$