Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for the exact value of
x.

log_(5)(4x)-2log_(5)(4)=1
Answer:

Solve for the exact value of $x$ . $\newline$ $\log _{5}(4 x)-2 \log _{5}(4)=1$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Product property of logarithms

Full solution

Q. Solve for the exact value of

x

.

\newline

\log _{5}(4 x)-2 \log _{5}(4)=1

\newline

Answer:

Apply Power Rule: Apply the power rule of logarithms to the term $2\log_5(4)$ . The power rule states that $n\log_b(a) = \log_b(a^n)$ . Therefore, we can rewrite the equation as: $\log_5(4^x) - \log_5(4^2) = 1$
Simplify Term: Simplify the term $4^2$ . Calculating $4^2$ gives us $16$ . So the equation now becomes: $\log_5(4x) - \log_5(16) = 1$
Apply Quotient Rule: Apply the quotient rule of logarithms to combine the logarithms on the left side. $\newline$ The quotient rule states that $\log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right)$ . Therefore, we can combine the logarithms: $\newline$ $\log_5\left(\frac{4x}{16}\right) = 1$
Simplify Fraction: Simplify the fraction inside the logarithm. $\newline$ Simplifying $\frac{4x}{16}$ gives us $\frac{x}{4}$ . So the equation now becomes: $\newline$ $\log_5\left(\frac{x}{4}\right) = 1$
Convert to Exponential Form: Convert the logarithmic equation to its exponential form. $\newline$ Using the definition of a logarithm, we can rewrite the equation as: $\newline$ $5^1 = \frac{x}{4}$
Solve for x: Solve for x. $\newline$ Multiplying both sides by $4$ to isolate $x$ gives us: $\newline$ $x = 5 \times 4$ $\newline$ $x = 20$

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