Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Condense the logarithm

y log c+z log q
Answer:
log(◻)

Condense the logarithm $\newline$ $y \log c+z \log q$ $\newline$ Answer: $\log (\square)$

View step-by-step help

View step-by-step help

Evaluate logarithms using properties

Full solution

Q. Condense the logarithm

\newline

y \log c+z \log q

\newline

Answer:

\log (\square)

Identify Properties: Identify the properties of logarithms that can be used to condense the expression $y \log c + z \log q$ . The power property of logarithms states that $n \cdot \log_b(x) = \log_b(x^n)$ . We can use this property to rewrite the given expression.
Apply Power Property: Apply the power property to each term of the expression. $\newline$ $y \log c$ can be rewritten as $\log c^y$ and $z \log q$ can be rewritten as $\log q^z$ . $\newline$ So, $y \log c + z \log q$ becomes $\log c^y + \log q^z$ .
Combine Terms: Use the product property of logarithms to combine the two logarithms into one. $\newline$ The product property states that $\log_b(x) + \log_b(y) = \log_b(xy)$ . We can apply this property to the expression $\log c^y + \log q^z$ . $\newline$ So, $\log c^y + \log q^z$ becomes $\log (c^y \cdot q^z)$ .
Write Final Expression: Write the final condensed logarithm expression. $\newline$ The final expression is $\log (c^y \cdot q^z)$ .

More problems from Evaluate logarithms using properties

Question

Write the exponential equation in logarithmic form.

\newline

9^3 = 729

\newline

\log_\square 729 = 3

Posted 2 months ago

Question

Write the exponential equation in logarithmic form.

\newline

e^4 \approx 54.598

\newline

\ln\_\_\_\_ \approx 4

Posted 2 months ago

Question

Write the logarithmic equation in exponential form.

\newline

\log_{10}100 = 2

\newline

10^2 = \underline{\hspace{2em}}

Posted 2 months ago

Question

Evaluate. Write your answer as a whole number, proper fraction, or improper fraction in simplest form.

\newline

\frac{\ln (e)}{10} =

Posted 2 months ago

Question

Rewrite as a quotient of two common logarithms. Write your answer in simplest form.

\newline

\log_3 33 =

Posted 2 months ago

Question

Evaluate. Round your answer to the nearest thousandth.

\newline

\log_{5}50 =

Posted 2 months ago

Question

Which property of logarithms does this equation demonstrate?

\newline

\log_3 3 + \log_3 6 = \log_3 18

\newline

\newline

\text{Product Property}

\newline

\text{Power Property}

\newline

\text{Quotient Property}

Posted 2 months ago

Question

Expand the logarithm. Assume all expressions exist and are well-defined.

\newline

Write your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable.

\newline

\log(uv)

\newline

Posted 2 months ago

Question

Expand the logarithm. Assume all expressions exist and are well-defined.

\newline

Write your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable.

\newline

\log v^7

\newline

Posted 2 months ago

Question

Expand the logarithm. Assume all expressions exist and are well-defined.

\newline

Write your answer as a sum or difference of base-

6

logarithms or multiples of base-

6

logarithms. The inside of each logarithm must be a distinct constant or variable.

\newline

\log_6 w^6

\newline

Posted 2 months ago