Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

log_(2)1024=

$\log _{2} 1024=$

View step-by-step help

View step-by-step help

Evaluate logarithms using properties

Full solution

Q.

\log _{2} 1024=

Identify relationship between base and number: Identify the relationship between the base of the logarithm and the number. $\newline$ The base of the logarithm is $2$ , and we need to find the power to which $2$ must be raised to get $1024$ .
Express number as power of base: Express $1024$ as a power of $2$ . $\newline$ $1024$ is a power of $2$ , and we can find this power by repeatedly dividing $1024$ by $2$ . $\newline$ $1024 = 2^{10}$ because $2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 1024$ .
Apply definition of logarithm: Apply the definition of a logarithm. $\newline$ Using the definition of a logarithm, $\log_{2}1024$ is the power to which the base $2$ must be raised to produce $1024$ . $\newline$ Since we found that $1024 = 2^{10}$ , $\log_{2}1024 = 10$ .

More problems from Evaluate logarithms using properties

Question

\newline

\frac{5}{6} \div \frac{9}{4}=

Posted 3 months ago

Question

\newline

\frac{8}{3} \div \frac{5}{3}=

Posted 3 months ago

Question

\newline

\frac{5}{4} \div \frac{3}{5}=

Posted 3 months ago

Question

\newline

\frac{3}{4} \div \frac{3}{4}=

Posted 3 months ago

Question

Write the expression in exponential form.

\newline

6 \times 6 \times 6 \times 6 \times 6=

Posted 3 months ago

Question

Write the expression in exponential form.

\newline

9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9=

Posted 3 months ago

Question

The value of Vishal's car is depreciating exponentially.

\newline

The relationship between

V

, the value of his car, in dollars, and

t

, the elapsed time, in years, since he purchased the car is modeled by the following equation.

\newline

V=22,500 \cdot 10^{-\frac{t}{12}}

\newline

How many years after purchase will Vishal's car be worth

\$ 10,000

\newline

Give an exact answer expressed as a base

-10

\newline

Posted 3 months ago

Question

A scientist measures the initial amount of Carbon

-14

in a substance to be

25

\newline

The relationship between

A

, the amount of Carbon

-14

remaining in that substance, in grams, and

t

, the elapsed time, in years, since the initial measurement is modeled by the following equation.

\newline

A=25 e^{-0.00012 t}

\newline

In how many years will the substance contain exactly

20

(\mathrm{g})

-14

\newline

Give an exact answer expressed as a natural logarithm.

\newline

Posted 3 months ago

Question

Which of the following is equivalent to

\log _{7}(a) \cdot \log _{b}(7)

\newline

1

\newline

\log (7)

\newline

\log (7 a)

\newline

\log _{a}(b)

\newline

\log _{b}(a)

Posted 3 months ago

Question

Which of the following is equivalent to

\log (a) \cdot \log _{a}(5)

\newline

1

\newline

\log (a)

\newline

\log (5)

\newline

\log (5 a)

\newline

\log _{a}(5 a)

Posted 3 months ago