Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write the expression
ln 2+ln 3 as a single logarithm in simplest form without any negative exponents.
Answer:
ln(◻)

Write the expression $\ln 2+\ln 3$ as a single logarithm in simplest form without any negative exponents. $\newline$ Answer: $\ln (\square)$

View step-by-step help

View step-by-step help

Change of base formula

Full solution

Q. Write the expression

\ln 2+\ln 3

as a single logarithm in simplest form without any negative exponents.

\newline

Answer:

\ln (\square)

Apply logarithm product rule: Apply the logarithm product rule. $\newline$ The logarithm product rule states that the sum of two logarithms with the same base is equal to the logarithm of the product of their arguments. $\newline$ So, $\ln 2 + \ln 3$ can be combined into a single logarithm as follows: $\newline$ $\ln(2 \times 3)$
Perform multiplication inside logarithm: Perform the multiplication inside the logarithm. $\newline$ Now, we multiply the numbers inside the logarithm to simplify the expression. $\newline$ $2 \times 3 = 6$ $\newline$ So, $\ln(2 \times 3)$ becomes $\ln(6)$ .
Write final answer: Write the final answer. $\newline$ The expression $\ln 2 + \ln 3$ has been simplified to $\ln(6)$ without any negative exponents.

More problems from Change of base formula

Question

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

\newline

5^x=1

\newline

x=

Posted 3 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 3 months ago

Question

Use the following function rule to find

f(1)

\newline

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

\newline

f(1) =

Posted 2 months 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 3 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 3 months ago

Question

Solve. Simplify your answer.

\newline

7\log x = 7

\newline

x =

Posted 2 months 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 3 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 3 months ago