https://file.aiquickdraw.com/mathbot/file/17273069244927n1rain3.jpg

Let's solve the problems shown in the image one by one.

### Problem 4:
\[
\log_5{5} = x
\]
This equation means "what exponent do we raise 5 to in order to get 5?" The answer is 1, because \(5^1 = 5\). Therefore:
\[
x = 1
\]

### Problem 5:
\[
\log_5{(x + 15)} = 2
\]
This equation means "5 raised to what power equals \(x + 15\)?" From the logarithmic definition:
\[
x + 15 = 5^2
\]
\[
x + 15 = 25
\]
Now, solve for \(x\):
\[
x = 25 - 15 = 10
\]
Thus, \(x = 10\).

### Problem 6:
\[
12^{\log_{12}{3}} = x
\]
Using the logarithmic identity \(a^{\log_a{b}} = b\), we can simplify the expression:
\[
12^{\log_{12}{3}} = 3
\]
Thus, \(x = 3\).

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Would you like any further details or clarifications on these problems?

### Relative Questions:
1. What is the general rule for solving logarithmic equations like these?
2. How can logarithmic properties simplify equations involving different bases?
3. What are the key logarithmic identities that help in solving such problems?
4. How do we solve logarithmic equations with different bases on both sides?
5. Can we use logarithms to solve exponential equations in general?

### Tip:
When solving logarithmic equations, always remember that the base of the logarithm and the argument must be positive and the base must be greater than 1.

Solve the following logarithmic problems:
1. log5(5) = x
2. log5(x + 15) = 2
3. 12^(log12(3)) = x

This page explains how to solve logarithmic equations like log5(5) = x, log5(x + 15) = 2, and 12^(log12(3)) = x using logarithmic identities and exponentiation rules. Detailed solutions are provided for each problem, suitable for students in Grades 9-12.

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