Rewrite the following in the form log(c). log(20)-log(5)

Given expression: We are given log(20) - log(5). To simplify this expression, we can use the quotient property of logarithms, which states that the difference of two logarithms with the same base is the logarithm of the quotient of their arguments. Quotient property: log_b(P) - log_b(Q) = log_b(P/Q)Apply quotient property: Apply the quotient property to log(20) - log(5): log(20) - log(5) = log(20/5)Calculate quotient: Calculate the quotient 20/5: 20/5 = 4Replace quotient in logarithm: Replace the quotient in the logarithm: log(20/5) = log(4)Final result: We have now rewritten log(20) - log(5) in the form log(c) where c = 4.

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Rewrite the following in the form
log(c).

log(20)-log(5)

Rewrite the following in the form $\log (c)$ . $\newline$ $\log (20)-\log (5)$

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Math Problems

Algebra 2

Evaluate logarithms using properties

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Q. Rewrite the following in the form

\log (c)

\newline

\log (20)-\log (5)

Given expression: We are given $\log(20) - \log(5)$ . To simplify this expression, we can use the quotient property of logarithms, which states that the difference of two logarithms with the same base is the logarithm of the quotient of their arguments. $\newline$ Quotient property: $\log_b(P) - \log_b(Q) = \log_b\left(\frac{P}{Q}\right)$
Apply quotient property: Apply the quotient property to $\log(20) - \log(5)$ : $\log(20) - \log(5) = \log\left(\frac{20}{5}\right)$
Calculate quotient: Calculate the quotient $20/5$ : $\newline$ $20/5 = 4$
Replace quotient in logarithm: Replace the quotient in the logarithm: $\log(\frac{20}{5}) = \log(4)$
Final result: We have now rewritten $\log(20) - \log(5)$ in the form $\log(c)$ where $c = 4$ .