Here are some exercises where you'll need to solve for $x$ in logarithmic equations like the ones you mentioned:

1. Solve for $x$:

$\log_2(x) = 3$ (Find the value of $x$).

2. Solve for $x$:

$\log_{10}(x) = 2$ (Find the value of $x$).

3. Solve for $x$:

$\log_5(x) = -1$ (Find the value of $x$).

4. Solve for $x$:

$\log_3(x) = 4$ (Find the value of $x$).

5. Solve for $x$:

$\log_7(x) = 2.5$ (Find the value of $x$).

6. Solve for $x$:

$\log_2(x) + \log_2(4) = 6$ (Find the value of $x$).

7. Solve for $x$:

$\log_4(x) = 3$ (Find the value of $x$).

8. Solve for $x$:

$\log_3(x^2) = 6$ (Find the value of $x$).

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Would you like a step-by-step solution to any of these problems or need more clarification?

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Related Questions:

1. How do logarithms with different bases work in equations?
2. How do you solve logarithmic equations with exponents (e.g., $\log_b(x^n)$)?
3. How do you combine logarithms in equations (e.g., using the property $\log_b(a) + \log_b(b) = \log_b(ab)$)?
4. How do you solve exponential equations like $2^x = 8$?
5. What is the change of base formula and when is it useful?

Tip: When solving logarithmic equations, remember that $\log_b(x) = y$ is equivalent to $b^y = x$.