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.