Answer :

To solve the problem of finding [tex]\( m \)[/tex] in the expression [tex]\( 600 = 5^m \)[/tex], we need to equate and evaluate the exponential equation using logarithms.

Here’s a step-by-step breakdown:

1. Equation Setup:
We are given the equation [tex]\( 600 = 5^m \)[/tex]. Our goal is to find the value of [tex]\( m \)[/tex] that satisfies this equation.

2. Use Logarithms:
To solve for [tex]\( m \)[/tex], apply logarithms to both sides of the equation. This is useful because logarithms allow us to bring the exponent down where it can be solved directly. Here, we'll use the common logarithm (though any base can technically be used):

[tex]\[
\log(600) = \log(5^m)
\][/tex]

3. Apply the Power Rule for Logarithms:
The power rule states that [tex]\( \log(a^b) = b \cdot \log(a) \)[/tex]. By applying this rule, the equation becomes:

[tex]\[
\log(600) = m \cdot \log(5)
\][/tex]

4. Isolate [tex]\( m \)[/tex]:
To solve for [tex]\( m \)[/tex], divide both sides by [tex]\( \log(5) \)[/tex]:

[tex]\[
m = \frac{\log(600)}{\log(5)}
\][/tex]

5. Calculate the Values:
Now you calculate or look up the values of the logarithms. The actual computation yields:

- [tex]\( \log(600) \approx 2.778151 \)[/tex]
- [tex]\( \log(5) \approx 0.69897 \)[/tex]

6. Determine [tex]\( m \)[/tex]:
Plugging these values in the equation, you get:

[tex]\[
m \approx \frac{2.778151}{0.69897} \approx 3.9746358687061645
\][/tex]

This gives us the value of [tex]\( m \approx 3.9746358687061645 \)[/tex], showing that [tex]\( 600 \)[/tex] is approximately equal to [tex]\( 5 \)[/tex] raised to this power.

Thank you for reading the article 625 is the product of powers of 5 Find tex m tex in tex 625 5 m tex. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

Other Questions