China | Can You Solve This? | Math Olympiad | A-Maths Challenge: Solve 5k⋅5k⋅5k= 20 

Are you ready to tackle a mind-bending Math Olympiad question straight from China’s elite A-Maths problem sets? These types of exponential equations test your ability to simplify expressions and solve with logic and accuracy.

Today’s challenge:

5k⋅5k⋅5k = 20

At first glance, it might seem complex—but with the right algebraic approach, we can crack it step by step.

✅ Step-by-Step Solution

Step 1: Combine Like Terms Using Exponent Rules

When multiplying powers with the same base, you add the exponents:

= 5k⋅5k⋅5k

= 5^{k + k + k}

= 5^{3k}

So now the equation becomes:

5^{3k} = 20

Step 2: Apply Logarithms to Both Sides

To solve for kk, we take the logarithm of both sides. We’ll use base 10 (common logarithm):

log{5^(3k)} = log20

Using the rule log(a^b)=blog(a):

3k log(5) = log(20)

Step 3: Plug In Known Log Values

log(5) = approx 0.6989

log(20) = approx 1.3010

Now solve:

3k*(0.6989) = 1.3010

3k = 1.3010 / 0.6989

K = 1.8613 / 3

K = 0.6203

 

Final Answer

K= approx 0.620

 

📘 Why This Math Olympiad Problem Is Important

Solving exponential equations like this sharpens your skills in powers, logarithms, and algebraic manipulation. These are core skills in A-Maths, Olympiad-level math, and higher education entrance exams globally.

See Lecture Here!