Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Rewrite the following in the form
log(c).

log(12)-log(3)

Rewrite the following in the form $\log (c)$ . $\newline$ $\log (12)-\log (3)$

View step-by-step help

View step-by-step help

Evaluate logarithms using properties

Full solution

Q. Rewrite the following in the form

\log (c)

.

\newline

\log (12)-\log (3)

Identify properties of logarithms: Identify the properties of logarithms that can be used to simplify the expression $\log(12) - \log(3)$ . $\newline$ The difference of logarithms of two numbers equals the logarithm of their quotient. $\newline$ Quotient property: $\log_b (P) - \log_b (Q) = \log_b (\frac{P}{Q})$
Apply quotient property: Apply the quotient property of logarithms to the expression $\log(12) - \log(3)$ . $\log(12) - \log(3) = \log\left(\frac{12}{3}\right)$
Calculate the quotient: Calculate the quotient $12/3$ . $\newline$ $12/3 = 4$
Substitute the quotient: Substitute the quotient back into the logarithm. $\log(\frac{12}{3}) = \log(4)$
Check final simplified form: Check if the expression $\log(4)$ is the final simplified form. $\newline$ Since $4$ cannot be simplified further in terms of base $10$ logarithms, $\log(4)$ is the final answer.

More problems from Evaluate logarithms using properties

Question

\newline

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

Posted 4 months ago

Question

\newline

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

Posted 4 months ago

Question

\newline

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

Posted 4 months ago

Question

\newline

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

Posted 4 months ago

Question

Write the expression in exponential form.

\newline

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

Posted 4 months ago

Question

Write the expression in exponential form.

\newline

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

Posted 4 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 4 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 4 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 4 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 4 months ago