Rewrite the following in the form log(c). log(12)-log(3)

Identify properties of logarithms: Identify the properties of logarithms that can be used to simplify the expression log(12) - log(3). The difference of logarithms of two numbers equals the logarithm of their quotient. Quotient property: log_b (P) - log_b (Q) = log_b (P/Q)Apply quotient property: Apply the quotient property of logarithms to the expression log(12) - log(3). log(12) - log(3) = log(12/3)Calculate the quotient: Calculate the quotient 12/3. 12/3 = 4Substitute the quotient: Substitute the quotient back into the logarithm. log(12/3) = log(4)Check final simplified form: Check if the expression log(4) is the final simplified form. Since 4 cannot be simplified further in terms of base 10 logarithms, log(4) is the final answer.

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Rewrite the following in the form
log(c).

log(12)-log(3)

Rewrite the following in the form $\log (c)$ . $\newline$ $\log (12)-\log (3)$

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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 (12)-\log (3)

Identify properties of logarithms: Identify the properties of logarithms that can be used to simplify the expression $\log(12) - \log(3)$ . $\newline$ The difference of logarithms of two numbers equals the logarithm of their quotient. $\newline$ Quotient property: $\log_b (P) - \log_b (Q) = \log_b (\frac{P}{Q})$
Apply quotient property: Apply the quotient property of logarithms to the expression $\log(12) - \log(3)$ . $\log(12) - \log(3) = \log\left(\frac{12}{3}\right)$
Calculate the quotient: Calculate the quotient $12/3$ . $\newline$ $12/3 = 4$
Substitute the quotient: Substitute the quotient back into the logarithm. $\log(\frac{12}{3}) = \log(4)$
Check final simplified form: Check if the expression $\log(4)$ is the final simplified form. $\newline$ Since $4$ cannot be simplified further in terms of base $10$ logarithms, $\log(4)$ is the final answer.