To solve the equation $6^x = 146$ by rewriting it in logarithmic form, we can follow these steps:

1. Rewrite the equation in logarithmic form. For an equation of the form $a^x = b$, the logarithmic form is $x = \log_a(b)$. $x = \log_6(146)$

2. Since calculators typically don’t have a base-6 logarithm function, we can use the change of base formula: $x = \frac{\log_{10}(146)}{\log_{10}(6)}$

3. Now, using a calculator to evaluate this:

   • $\log_{10}(146) \approx 2.1644$
   • $\log_{10}(6) \approx 0.7782$

   Therefore: $x \approx \frac{2.1644}{0.7782} \approx 2.78$

So, $x \approx 2.78$ to two decimal places.

To complete the answer in your system:

1. For the logarithmic form:

   • The base is $6$.
   • The number inside the logarithm is $146$.
   • This equals $x$.

2. For the value of $x$:

   • $x = 2.78$.

Would you like further details on this solution or have any questions?

Here are 5 related questions that expand on logarithmic functions:

1. How do you solve exponential equations with different bases?
2. What is the change of base formula, and why is it useful?
3. How can logarithmic functions be applied in real-world scenarios?
4. What are common properties of logarithms that help simplify complex expressions?
5. How does understanding logarithms assist in graphing exponential functions?

Tip: Remember that the change of base formula, $\log_a(b) = \frac{\log_c(b)}{\log_c(a)}$, is especially helpful when calculators don’t support certain logarithmic bases.