Rewrite the following in the form log(c). log(10)-log(5)

Identify Property of Logarithms: log(10) - log(5) Identify the property of logarithms that can be used to combine the terms. 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: log(10) - log(5) Apply the quotient property of logarithms. log(10) - log(5) = log(10/5)Simplify Fraction: Simplify the fraction 10/5. 10/5 simplifies to 2. So, log(10/5) = log(2)Rewrite Expression: Rewrite the expression in the form log(c). log(2) is already in the form log(c) where c = 2.

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Rewrite the following in the form
log(c).

log(10)-log(5)

Rewrite the following in the form $\log (c)$ . $\newline$ $\log (10)-\log (5)$

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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 (10)-\log (5)

Identify Property of Logarithms: $\log(10) - \log(5)$ $\newline$ Identify the property of logarithms that can be used to combine the terms. $\newline$ 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: $\log(10) - \log(5)$ $\newline$ Apply the quotient property of logarithms. $\newline$ $\log(10) - \log(5) = \log\left(\frac{10}{5}\right)$
Simplify Fraction: Simplify the fraction $\frac{10}{5}$ . $\newline$ $\frac{10}{5}$ simplifies to $2$ . $\newline$ So, $\log\left(\frac{10}{5}\right) = \log(2)$
Rewrite Expression: Rewrite the expression in the form $\log(c)$ . $\log(2)$ is already in the form $\log(c)$ where $c = 2$ .