if log10(5)=x, find the value of log2(5) in terms of x

We are given that:

\[
\log_{10}(5) = x
\]

We need to find \(\log_2(5)\) in terms of \(x\). We can use the **change of base formula** for logarithms, which states:

\[
\log_b(a) = \frac{\log_c(a)}{\log_c(b)}
\]

In our case, we want to convert \(\log_2(5)\) into terms of base 10 logarithms. So, we can express \(\log_2(5)\) as:

\[
\log_2(5) = \frac{\log_{10}(5)}{\log_{10}(2)}
\]

But we know from the problem that \(\log_{10}(5) = x\), so we substitute this:

\[
\log_2(5) = \frac{x}{\log_{10}(2)}
\]

Thus, the value of \(\log_2(5)\) in terms of \(x\) is:

\[
\boxed{\frac{x}{\log_{10}(2)}}
\]

Would you like more details on this solution?

### Related Questions:
1. How do you use the change of base formula for different logarithms?
2. Can you express \(\log_2(5)\) in terms of natural logarithms instead of base 10?
3. How do you calculate \(\log_{10}(2)\) approximately?
4. What is the relationship between logarithms with different bases?
5. How can you convert between logarithms of any two arbitrary bases?

### Tip:
When solving logarithmic problems, the change of base formula is one of the most powerful tools for converting between different logarithmic bases.

If log10(5) = x, find the value of log2(5) in terms of x.

Discover how to express log2(5) in terms of log10(5) using the change of base formula. This detailed explanation covers logarithmic transformations and shows how log10(5) = x leads to the solution. Suitable for students in Grades 9-12.

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