https://file.aiquickdraw.com/mathbot/file/1725503167141na37jxk9.jpg

The expression in the image is showing the change of base formula for logarithms. The given expression:

\[
^2\log 7
\]

can be rewritten using the change of base formula as:

\[
^2\log 7 = \frac{\log 7}{\log 2}
\]

This formula allows you to express the logarithm of a number with a different base (in this case, base 2) in terms of natural logarithms (or logarithms to another base, often base 10). Specifically, it is the ratio of the logarithms of the argument (7) to the logarithm of the base (2).

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How do you apply the change of base formula for logarithms with different bases?
2. What are some practical applications of using logarithms with different bases?
3. Can the change of base formula be applied with natural logarithms (ln) as well?
4. How do you calculate logarithms without a calculator, using basic logarithmic rules?
5. Why is the change of base formula important in solving logarithmic equations?

**Tip:** Always remember that logarithms can be expressed in any base using the change of base formula, allowing flexibility in computations!

Rewrite the expression 2log7 using the change of base formula.

Learn how to apply the change of base formula to rewrite the expression 2log7. This involves using the logarithmic ratio of log 7 divided by log 2. Understand how to switch logarithmic bases effectively for solving complex logarithmic equations. Suitable for students in Grades 9-12.

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