To rewrite the exponential equation 3^x = 243 in logarithmic form, we first need to understand what logarithms are. A logarithm answers the question: to what power must a specific base be raised to produce a certain number?
In this case, we have a base of 3 and we want to find the value of x that satisfies the equation. The logarithmic form of the equation can be represented as:
log3(243) = x
This means that x is the power to which the base 3 must be raised to equal 243.
Next, we can convert 243 into a power of 3. We see that:
3^5 = 243
So, we can also express this logarithmic form as:
x = 5
If we want the logarithmic form in base 10, we can use the change of base formula:
log10(243) / log10(3) = x
This gives us the relationship in base 10 instead of base 3. Therefore, the logarithmic form in base 10 might look a bit different, but it conveys the same concept.