Resources

Resources

Bytelearn - cat image with glasses

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

View step-by-step help

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 $\log\left(\frac{b^q}{k^z}\right)$ .

More problems from Product property of logarithms

Question

Solve. Write your answer as an integer or a fraction in simplest form.

\newline

5^x=1

\newline

x=

Posted 2 months ago

Question

Steven opened a savings account and deposited

\$100.00

as principal. The account earns

9\%

interest, compounded annually. What is the balance after

5

\newline

Use the formula

A = P(1 + \frac{r}{n})^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years.

\newline

Round your answer to the nearest cent.

\newline

\$

Posted 2 months ago

Question

Use the following function rule to find

f(1)

\newline

f(x) = 12(7)^x + 8

\newline

f(1) =

Posted 1 month ago

Question

The town of Valley View conducted a census this year, which showed that it has a population of

1,800

people. Based on the census data, it is estimated that the population of Valley View will grow by

12\%

\newline

Write an exponential equation in the form

y = a(b)^x

that can model the town population,

y

x

decades after this census was taken.

\newline

Use whole numbers, decimals, or simplified fractions for the values of

a

b

\newline

y =

Posted 2 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = 9^x

\newline

x =

Posted 2 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = e^x

\newline

x =

Posted 1 month ago

Question

Solve. Simplify your answer.

\newline

\log u = 1

\newline

u =

Posted 2 months ago

Question

Solve. Simplify your answer.

\newline

7\log x = 7

\newline

x =

Posted 1 month ago

Question

g(t) = 3^t

change over the interval from

t = 3

t = 4

\newline

\newline

g(t)

3

\newline

g(t)

3

\newline

g(t)

3\%

\newline

g(t)

200\%

Posted 2 months ago

Question

f(x)

6

over every unit interval in

x

f(0) = 0

\newline

Which could be a function rule for

f(x)

\newline

\newline

f(x) = 6^x

\newline

f(x) = 6x

\newline

f(x) = \frac{1}{6^x}

\newline

f(x) = \frac{x}{6}

Posted 2 months ago