Question: 3. Solve the following equations
(a) log₇49 = x (b) logₓ10 = 1 (c) log√3 x = 2 (d) x^(logₓx) = 5.
4. Evaluate.
(a) 9^(log₉2) + 3^(log₃8) (b) log₄4⁵ × log₁₀10² (c) 7^(log₇9) + log₂(1/2)
(d) log₁/₂(1/8) - 4log₁₀10 (e) 10^(1 - log₁₀3)
1. **Problem Statement:** Solve the equations in 3(a) and evaluate the expressions in 4(a).
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### Problem 3(a): Solve $$\log_7 49 = x$$
2. **Formula and Rules:**
- The logarithm $$\log_b a = c$$ means $$b^c = a$$.
- Here, $$\log_7 49 = x$$ means $$7^x = 49$$.
3. **Intermediate Work:**
- Recognize that $$49 = 7^2$$.
- So, $$7^x = 7^2$$.
- By equality of exponents, $$x = 2$$.
4. **Answer:** $$x = 2$$.
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### Problem 4(a): Evaluate $$9^{\log_9 2} + 3^{\log_3 8}$$
5. **Formula and Rules:**
- For any base $$a$$ and number $$b$$, $$a^{\log_a b} = b$$.
6. **Intermediate Work:**
- $$9^{\log_9 2} = 2$$.
- $$3^{\log_3 8} = 8$$.
- So, the expression becomes $$2 + 8 = 10$$.
7. **Answer:** $$10$$.
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**Final answers:**
- For 3(a): $$x = 2$$.
- For 4(a): $$10$$.