Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify
e^(2ln 4-3) and write without any logarithms.
Answer:

Simplify $e^{2 \ln 4-3}$ and write without any logarithms. $\newline$ Answer:

View step-by-step help

View step-by-step help

Power property of logarithms

Full solution

Q. Simplify

e^{2 \ln 4-3}

and write without any logarithms.

\newline

Answer:

Apply Logarithm Property: Apply the property of logarithms that allows us to move the coefficient in front of the logarithm to the exponent inside the logarithm. $\newline$ Property: $a \cdot \ln(b) = \ln(b^a)$ $\newline$ Calculation: $2\ln(4)$ becomes $\ln(4^2)$ $\newline$ Math error check:
Simplify Inside Logarithm: Simplify the expression inside the logarithm. $\newline$ Calculation: $4^2 = 16$ $\newline$ Math error check:
Rewrite Using Simplified Logarithm: Rewrite the expression using the simplified logarithm. $\newline$ Calculation: $e^{\ln(16) - 3}$ $\newline$ Math error check:
Apply Exponent Property: Apply the property of logarithms and exponents that states $e^{\ln(x)} = x$ . $\newline$ Property: $e^{\ln(x)} = x$ $\newline$ Calculation: $e^{\ln(16)} = 16$ $\newline$ Math error check:
Combine Exponential and Constant Terms: Simplify the expression by combining the exponential and constant terms. $\newline$ Calculation: $16 \times e^{-3}$ $\newline$ Math error check:
Calculate Constant: Recognize that $e^{-3}$ is a constant that can be calculated. $\newline$ Calculation: $e^{-3} \approx 0.0498$ (rounded to four decimal places) $\newline$ Math error check:
Multiply to Get Final Answer: Multiply the constant $e^{-3}$ by $16$ to get the final answer. $\newline$ Calculation: $16 \times 0.0498 \approx 0.7968$ (rounded to four decimal places) $\newline$ Math error check:

More problems from Power 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