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 = (1/c) * log_b(a), we can simplify log_(5^3)5 to (1/3) * 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 (1/3) * 1, which simplifies to 1/3.Final Answer: So, log_(125)5 = 1/3. This is our final answer.

Resources

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$\log _{125} 5=$

View step-by-step help

Home

Math Problems

Grade 8

Relationship between squares and square roots

Full solution

\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.