Online Test — Logarithms
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
medium
Write \(3^4 = 81\) in logarithmic form
\(\log_3 81 = 4\)
\(\log_4 81 = 3\)
\(\log_3 4 = 81\)
\(\log_{81} 3 = 4\)
Explanation: Base 3, argument 81, exponent 4
Question 2 of 10
medium
Write \(\log_2 32 = 5\) in exponential form
\(2^5 = 32\)
\(5^2 = 32\)
\(2^{32} = 5\)
\(32^2 = 5\)
Explanation: base^log = argument
Question 3 of 10
medium
Evaluate \(\log_2 16\)
2
3
4
5
Explanation: 2⁴ = 16
Question 4 of 10
medium
Evaluate \(\log 1000\)
1
2
3
4
Explanation: 10³ = 1000
Question 5 of 10
medium
\(\log_5 1 = ?\)
0
1
5
undefined
Explanation: a⁰ = 1 for any a
Question 6 of 10
medium
Expand \(\log_3 (7 \times 9)\)
\(\log_3 7 + \log_3 9\)
\(\log_3 7 \times \log_3 9\)
\(\log_3 7 - \log_3 9\)
\(3\log_3 7\)
Explanation: Product law: log(mn)=log m+log n
Question 7 of 10
medium
Write as single log: \(\log x - \log y\)
\(\log(x-y)\)
\(\log(x+y)\)
\(\log(xy)\)
\(\log(x/y)\)
Explanation: Quotient law
Question 8 of 10
medium
Given \(\log 2 = 0.3010\), find \(\log 8\)
0.6020
0.9030
1.2040
2.4080
Explanation: 8=2³, so log8=3×0.3010=0.9030
Question 9 of 10
medium
If pH = -\(\log[H^+]\) and [H⁺] = \(10^{-7}\), pH = ?
5
6
7
8
Explanation: -(-7×log10)=7
Question 10 of 10
medium
Simplify \(\log_a a^5\)
1
5
a
5a
Explanation: Power law: 5 log_a a = 5×1=5