Write the expression below as a single logarithm in simplest form. log_(b)4-log_(b)4 Answer: log_(b)(◻)

Identify Property: Identify the property used to combine the logarithms. The expression log_(b)4 - log_(b)4 involves the subtraction of two logarithms with the same base and the same argument. The property that applies here is that the logarithm of any number minus itself is zero.Apply Property: Apply the property to combine the logarithms. Since log_(b)4 and log_(b)4 are the same, their difference is zero. log_(b)4 - log_(b)4 = 0Write Single Logarithm: Write the expression as a single logarithm. The expression 0 can be written as log_(b)1 because the logarithm of 1 to any base is 0. Therefore, log_(b)4 - log_(b)4 = log_(b)1

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Write the expression below as a single logarithm in simplest form.

log_(b)4-log_(b)4
Answer:
log_(b)(◻)

Write the expression below as a single logarithm in simplest form. $\newline$ $\log _{b} 4-\log _{b} 4$ $\newline$ Answer: $\log _{b}(\square)$

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Math Problems

Algebra 2

Quotient property of logarithms

Full solution

Q. Write the expression below as a single logarithm in simplest form.

\newline

\log _{b} 4-\log _{b} 4

\newline

Answer:

\log _{b}(\square)

Identify Property: Identify the property used to combine the logarithms. $\newline$ The expression $\log_{b}4 - \log_{b}4$ involves the subtraction of two logarithms with the same base and the same argument. $\newline$ The property that applies here is that the logarithm of any number minus itself is $0$ .
Apply Property: Apply the property to combine the logarithms. $\newline$ Since $\log_{b}4$ and $\log_{b}4$ are the same, their difference is zero. $\newline$ $\log_{b}4 - \log_{b}4 = 0$
Write Single Logarithm: Write the expression as a single logarithm. $\newline$ The expression $0$ can be written as $\log_{b}1$ because the logarithm of $1$ to any base is $0$ . $\newline$ Therefore, $\log_{b}4 - \log_{b}4 = \log_{b}1$