Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the following logarithm problem for the positive solution for
x.

log_(27)x=-(2)/(3)
Answer:

Solve the following logarithm problem for the positive solution for $x$ . $\newline$ $\log _{27} x=-\frac{2}{3}$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Quotient property of logarithms

Full solution

Q. Solve the following logarithm problem for the positive solution for

x

.

\newline

\log _{27} x=-\frac{2}{3}

\newline

Answer:

Understand the logarithmic equation: Understand the logarithmic equation. $\newline$ We have the equation $\log_{27}(x) = -\frac{2}{3}$ . We need to find the value of $x$ that satisfies this equation.
Convert to exponential form: Convert the logarithmic form to exponential form. $\newline$ The logarithmic equation $\log_{27} x$ can be rewritten in exponential form as $27^{\log_{27}(x)} = x$ . Using the given equation, we have $27^{-\left(\frac{2}{3}\right)} = x$ .
Calculate value of $27^{(-2/3)}$ : Calculate the value of $27$ raised to the power of negative two-thirds. $\newline$ Since $27$ is $3^3$ , we can rewrite $27^{(-\frac{2}{3})}$ as $(3^3)^{(-\frac{2}{3})}$ . By the power of a power rule, this simplifies to $3^{-2}$ , which is $\frac{1}{3^2}$ or $\frac{1}{9}$ .
Verify the solution: Verify the solution. $\newline$ We found that $x = \frac{1}{9}$ . To verify, we can plug this value back into the original equation and check if it holds true: $\log_{27}(\frac{1}{9}) = -\frac{2}{3}$ . Since $\frac{1}{9}$ is $3^{-2}$ and $27$ is $3^3$ , the logarithm simplifies to $-\frac{2}{3}$ , which matches the right side of the equation.

More problems from Quotient property of logarithms

Question

x

\newline

5^x=1

\newline

\newline

Write your answer in simplest form.

Posted 5 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.

Posted 4 months ago

Question

Use the following function rule to find

f(1)

\newline

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

Posted 5 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 8 months ago

Question

x

\newline

7 = 9^x

\newline

Round your answer to the nearest thousandth.

Posted 4 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = e^x

\newline

x =

Posted 7 months ago

Question

Solve. Simplify your answer.

\newline

\log u = 1

\newline

u =

Posted 9 months ago

Question

Solve. Simplify your answer.

\newline

7\log x = 7

\newline

x =

Posted 7 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 4 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) = 6x

\newline

f(x) = 6^x

\newline

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

\newline

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

Posted 4 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant