Introduction: This is a core topic in algebra. Mastering the laws of indices and logarithms is essential for solving many types of equations. Expect direct questions on solving for x, and be ready to apply these rules in other topics like Geometric Progressions.

The "S Pass" Foundation (නියත S එකකට)

• Prompt 1 (Recall): Write down the three main laws of indices (for multiplication, division, and power of a power).

• Prompt 2 (Convert): Write 3x2​ in index form.

• Prompt 3 (Calculate): Find the value of 6432​.

• Prompt 4 (Solve): Solve the equation 3x=81.

• Prompt 5 (Recall): Write down the three main laws of logarithms (for addition, subtraction, and powers).

Climbing to a "C" (C එකට පාර)

• Prompt 1 (Calculate): Find the value of (1258​)−32​.

• Prompt 2 (Solve): Solve the equation 4x−1=32.

• Prompt 3 (Simplify): Simplify: 2log10​5+log10​4.

• Prompt 4 (Solve): Solve for x: log2​40−log2​5=log2​x.

• Prompt 5 (Simplify): Simplify and express with positive indices: (a−3​)2÷a−2.

Aiming for a "B" (B ඉලක්කය)

• Prompt 1 (Solve): Solve the equation 92x−1×271−x=1.

• Prompt 2 (Solve): Solve for x: 2loga​3+loga​4=loga​x+loga​6.

• Prompt 3 (Problem Solve): If 3x=p and 3y=q, express log3​(pq2) in terms of x and y.

• Prompt 4 (Justify): Without using a calculator, prove that log5​50+log5​2−log5​4=2.

• Prompt 5 (Application): The third term of a geometric progression is a5 and the fifth term is a9. If the first term is a, find the common ratio in terms of a.

Securing the "A" Distinction (A සාමාර්ථය තහවුරු කරගන්න)

• Prompt 1 (Challenge Solve): Solve for x: (4x)−5(2x)+4=0. (Hint: Let y=2x).

• Prompt 2 (Proof): Show that lg4+lg6lg8+lg9​=lg6. Is this statement correct? Justify your answer. (This is a trick question to test understanding of laws).

• Prompt 3 (Derive): If logx​a=2 and logy​a=3, find the value of logxy​a.

• Prompt 4 (Complex Solve): Solve for x: 32x+1−28(3x)+9=0.

• Prompt 5 (Synthesis): If lg(3x+y​)=21​(lgx+lgy), show that yx​+xy​=7.