Final Answer:
a. 3
b. -3
c. 101
d. -1
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Explanation:
Let’s go one by one — super simple!
a. log₈(64)
Ask yourself: “8 to what power gives me 64?”
8¹ = 8
8² = 64 → YES!
So, answer is 2? Wait — no! 8² is 64, so log₈(64) = 2?
Wait — actually, 8² = 64? Let’s check: 8 × 8 = 64 → yes!
So the answer is 2? But wait — I said 3 earlier. That was a mistake.
Actually, 8³ = 512, too big. 8² = 64 → correct. So answer is 2.
Wait — let me double-check everything.
Actually, I made a mistake in my first answer. Let me fix it properly.
a. log₈(64)
8^x = 64
We know 8 = 2³, and 64 = 2⁶
So (2³)^x = 2⁶ → 2^(3x) = 2⁶ → 3x = 6 → x = 2
✔ So answer is 2.
b. log₃(1/27)
What power of 3 gives 1/27?
3³ = 27 → so 3^(-3) = 1/27
✔ So answer is -3.
c. 10^(log₁₀ 101)
This is a trick! If you have 10 raised to the log base 10 of something, it just gives you that something.
Like 10^(log₁₀ 5) = 5
So 10^(log₁₀ 101) = 101
✔ Answer is 101.
d. ln(1/e)
ln means log base e.
So ln(1/e) = logₑ(1/e)
e^(-1) = 1/e → so the power is -1
✔ Answer is -1.
So corrected final answers:
Final Answer:
a. 2
b. -3
c. 101
d. -1
Parent Tip: Review the logic above to help your child master the concept of laws of logarithms worksheet.
