Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

log_(125)5=

$\log _{125} 5=$

View step-by-step help

View step-by-step help

Relationship between squares and square roots

Full solution

Q.

\log _{125} 5=

Find Exponent Value: We need to find the value of $\log_{125}5$ . This means we are looking for the exponent that $125$ must be raised to in order to get $5$ .
Rewrite in Base $5$ : We know that $125$ is equal to $5^3$ . So we can rewrite the logarithm in terms of base $5$ : $\log_{5^3}5$ .
Simplify Using Property: Using the property of logarithms that $\log_{b^c}a = \frac{1}{c} \cdot \log_b(a)$ , we can simplify $\log_{5^3}5$ to $\frac{1}{3} \cdot \log_5(5)$ .
Solve for $\log 5$ : We know that $\log_b(b) = 1$ for any base $b$ , because any number raised to the power of $1$ is itself. Therefore, $\log_5(5) = 1$ .
Substitute and Simplify: Substituting the value from the previous step, we get $(\frac{1}{3}) \times 1$ , which simplifies to $\frac{1}{3}$ .
Final Answer: So, $\log_{125}5 = \frac{1}{3}$ . This is our final answer.

More problems from Relationship between squares and square roots

Question

\sqrt{49}

?

\newline

Posted 1 month ago

Question

Complete the following statement. Use the integers that are closest to the number in the middle.

\newline

<

\sqrt{40}

<

Posted 1 month ago

Question

-\sqrt{64}

\newline

Posted 2 months ago

Question

\sqrt[3]{27}

Posted 1 month ago

Question

Which two integers is

-\sqrt{48}

\newline

\newline

[A]-6 \text{ and } -5

\newline

[B]5 \text{ and } 6

\newline

[C]-7 \text{ and } -6

\newline

[D]6 \text{ and } 7

Posted 6 days ago

Question

What is the cube root of

-64

\newline

Posted 2 months ago

Question

Which two integers is

\sqrt[3]{22}

\newline

\newline

[1 \text{ and } 2]

\newline

[15 \text{ and } 16]

\newline

[16 \text{ and } 17]

\newline

[2 \text{ and } 3]

Posted 2 months ago

Question

\newline

(\sqrt{25})^2 = \_\_\_\_\_

Posted 1 month ago

Question

Look at this equation:

\newline

c^3 = 27

\newline

\newline

c

, the cube root of

27

\newline

c =

\newline

Posted 2 months ago

Question

Write the sentence as an equation.

\newline

172

is equal to the quotient of

x

4

\newline

/

) if you want to use a division sign.

\newline

Posted 1 month ago