To solve these problems, we need to understand logarithmic equations. Here’s the approach:

Problem (a)

We are given: $\log_3 x = 7$ To find $x$, rewrite this in exponential form: $x = 3^7$ Now calculate $3^7$: $3^7 = 2187$ So, $x = 2187$.

Problem (b)

We are given: $\log_7 x = 5$ Rewrite this in exponential form: $x = 7^5$ Now calculate $7^5$: $7^5 = 16807$ Thus, $x = 16807$.

Answers

• (a) $x = 2187$
• (b) $x = 16807$

Would you like more details on logarithmic conversions, or do you have any questions?

Here are five related questions to expand on this topic:

1. How do you convert a logarithmic equation to exponential form?
2. What are some common logarithmic properties that are useful for solving equations?
3. How can you solve logarithmic equations with different bases?
4. How do you calculate large powers efficiently?
5. What is the relationship between exponential and logarithmic functions?

Tip: To solve logarithmic equations, always try to rewrite them in exponential form to simplify the problem.