Condense the logarithm q log b-z log k Answer: log(◻)

Identify Property: Identify the property of logarithm used to condense q log b - z log k. The expression q log b - z log k suggests that we need to use the power and quotient properties of logarithms to condense the expression into a single logarithm.Apply Power Property: Apply the power property to rewrite q log b and z log k. The power property of logarithms states that n log(a) = log(a^n). We can apply this property to both terms. q log b becomes log(b^q) and z log k becomes log(k^z).Apply Quotient Property: Apply the quotient property to combine log(b^q) and log(k^z). The quotient property of logarithms states that log(a) - log(b) = log(a/b). We can apply this property to combine the two logarithms into one. log(b^q) - log(k^z) becomes log((b^q)/(k^z)).Write Final Answer: Write the final answer. The condensed form of the logarithm is log((b^q)/(k^z)).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Condense the logarithm

q log b-z log k
Answer:
log(◻)

Condense the logarithm $\newline$ $q \log b-z \log k$ $\newline$ Answer: $\log (\square)$

View step-by-step help

Home

Math Problems

Precalculus

Product property of logarithms

Full solution

Q. Condense the logarithm

\newline

q \log b-z \log k

\newline

Answer:

\log (\square)

Identify Property: Identify the property of logarithm used to condense $q \log b - z \log k$ . The expression $q \log b - z \log k$ suggests that we need to use the power and quotient properties of logarithms to condense the expression into a single logarithm.
Apply Power Property: Apply the power property to rewrite $q \log b$ and $z \log k$ . The power property of logarithms states that $n \log(a) = \log(a^n)$ . We can apply this property to both terms. $q \log b$ becomes $\log(b^q)$ and $z \log k$ becomes $\log(k^z)$ .
Apply Quotient Property: Apply the quotient property to combine $\log(b^q)$ and $\log(k^z)$ . The quotient property of logarithms states that $\log(a) - \log(b) = \log(\frac{a}{b})$ . We can apply this property to combine the two logarithms into one. $\log(b^q) - \log(k^z)$ becomes $\log(\frac{b^q}{k^z})$ .
Write Final Answer: Write the final answer. $\newline$ The condensed form of the logarithm is $\log\left(\frac{b^q}{k^z}\right)$ .