Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

log_(5)3125=

$\log _{5} 3125=$

View step-by-step help

View step-by-step help

Evaluate logarithms using properties

Full solution

Q.

\log _{5} 3125=

Identify Base and Number: Identify the base of the logarithm and the number whose logarithm is to be found. $\newline$ The base is $5$ , and the number is $3125$ .
Check Power of $5$ : Determine if $3125$ can be expressed as a power of $5$ . $3125$ is $5$ raised to some power because $5$ is a prime number and $3125$ is a multiple of $5$ .
Find Power of $5$ : Find the power to which $5$ must be raised to get $3125$ . By trial, $5^5 = 3125$ .
Write as Power of $5$ : Write $3125$ as a power of $5$ in the logarithmic expression. $\newline$ $\log_{5}3125$ becomes $\log_{5}(5^5)$ .
Apply Power Property: Apply the power property of logarithms. $\newline$ The power property states that $\log_b(a^n) = n \cdot \log_b(a)$ . $\newline$ Therefore, $\log_{5}(5^5)$ becomes $5 \cdot \log_{5}5$ .
Evaluate Logarithm: Evaluate $\log_{5}5$ . The logarithm of a number to the same base is $1$ . So, $\log_{5}5$ is $1$ .
Multiply Exponent: Multiply the exponent by the logarithm of the base to the same base. $5 \times \log_{5}5$ becomes $5 \times 1$ .
Calculate Final Result: Calculate the final result. $\newline$ $5 \times 1$ equals $5$ .

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