The image you provided contains logarithmic problems. Let's break down each question step by step.

6. Gunakan sifat $a^{\log_b b} = b$ untuk menentukan hasil dari ekspresi berikut:

(Use the property $a^{\log_b b} = b$ to find the result of the following expressions)

a. $100^{\log_6 6}$

• Since $a^{\log_b b} = b$, this expression simplifies to 6.

b. $32^{\log_2 2}$

• Applying the same property, the result is 2.

c. $25^{\log_5 5}$

• Simplifying, the result is 5.

d. $4^{\log_8 8}$

• Simplifies to 8.

7. Gunakan sifat-sifat logaritma untuk menentukan hasil dari ekspresi berikut:

(Use logarithmic properties to find the result of the following expressions)

a. $2 \log 128 + 2 \log 9$

• Using the property $n \log a = \log a^n$, this becomes: $\log 128^2 + \log 9^2 = \log 16384 + \log 81 = \log (16384 \times 81) = \log 1327104$ Result: $\log 1327104$.

b. $\log_3 9 - \frac{1}{2} \log_8 8 + 2 \log_6 6 - \log_3 27$

• Using properties: $\log_3 9 = 2, \quad \frac{1}{2} \log_8 8 = \frac{1}{2} \cdot 1 = \frac{1}{2}, \quad 2 \log_6 6 = 2 \cdot 1 = 2, \quad \log_3 27 = 3$ Result: $2 - \frac{1}{2} + 2 - 3 = 0.5$.

c. $4 \log_7 7 - 8 \log_5 5 + 3 \log_8 8$

• Simplifying: $4 \log_7 7 = 4, \quad 8 \log_5 5 = 8, \quad 3 \log_8 8 = 3$ Result: $4 - 8 + 3 = -1$.

8. Ubah bentuk logaritma berikut menjadi bentuk eksponen, lalu tentukan nilai $x$ yang memenuhi:

(Convert the following logarithmic forms to exponential forms and determine the value of $x$)

a. $\log x = 3$

• Rewrite as $x = 10^3$.
• Therefore, $x = 1000$.

b. $3 \log (2x + 1) = 2$

• Divide both sides by 3: $\log (2x + 1) = \frac{2}{3}$
• Rewrite as an exponential: $2x + 1 = 10^{\frac{2}{3}}$ Solve for $x$.

c. $\frac{1}{4} \log (6x - 5) = -1$

• Multiply both sides by 4: $\log (6x - 5) = -4$
• Rewrite as: $6x - 5 = 10^{-4}$ Solve for $x$.

Would you like more detailed solutions for any of these steps?

Here are 5 additional related questions to deepen your understanding:

1. How do you simplify logarithmic expressions using properties like the product, quotient, and power rules?
2. Can you explain how to solve equations involving logarithms and exponents?
3. What is the significance of the change of base formula in logarithms?
4. How do you interpret a logarithmic equation when solving for unknown values?
5. Can you convert between logarithmic and exponential forms for any base?

Tip: Remember that logarithms and exponents are inverse operations, so understanding their relationship is key to solving many algebraic problems.